In this chapter, Elijah departs to heaven and Elisha succeeds him as prophet.
There is a progression of several events in this chapter, all relating to the transition that happens between Elijah and Elisha. Most of this chapter is intended to establish Elisha's prophetic authority as he takes up Elijah's mantle both literally and figuratively.
This is not the first transition of power we have observed in the bible. I think the most significant transition we saw in the past was when Joshua took leadership of Israel after the death of Moses (most clearly marked out in Joshua 1). In addition, we saw a transition happen between David and his son Solomon (which was marked by a brief political conflict between Solomon and Adonijah in 1 Kings 1). I am calling these out because for the most part, they were peaceful and intentional transitions, rather than e.g. David taking power from Ish-Bosheth by force (2 Samuel 2-4) or the split that happened between Jeroboam and Rehoboam (1 Kings 12).
I think the closest parallel to what happens in this chapter is the transition between Moses and Joshua. In that case (as with Elijah and Elisha) there was no family relationship between them: Joshua was a servant and student of Moses, and Moses was a sort of mentor to him. Similarly, the prophets in this chapter call Elijah the master of Elisha and I think it's fair to say that Elijah was training Elisha to be his replacement since Elijah himself anointed Elisha to be the next prophet. Even the similarity of their names (which is undoubtedly confusing to first-time bible readers) is possibly intended to evoke the similarity of their callings and ministry, and they certainly perform a lot of the same miracles.
Speaking of names, Elisha and Joshua also have similar names. Elisha means "God saves", while Joshua means "the LORD saves". Another similarity between Elisha and Joshua is the symbolic power of crossing the Jordan. Moses dies outside of the promised land and one of Joshua's first acts as leader is to take the nation across the Jordan, which miraculously splits to permit them to cross. Here, Elijah leads Elisha out of the promised land, is taken up into heaven, and Elisha's first act as prophet is to split the waters again and cross back into the land of Israel.
That said, the transition of power between Elijah and Elisha is a much more finely crafted story than what happened between Moses and Joshua, so I think it is instructive for us to explore the details a bit.
The first thing that happens is Elijah travels around to three different areas in the northern kingdom, Israel, and every time he tries to dissuade Elisha from following him, and the first two times there is a group of prophets that tell Elisha his master is going to depart that day, and every time Elisha tells them that while they prophesy truthfully, that they should be silent and not say that thing to him. So, what does this mean? Why does Elijah try to get away from Elisha, and why does Elisha respond to the prophets the way that he does?
Rashi suggests that Elijah was trying to drive away Elisha out of his humility, so that Elisha would not see him be taken away. That may be part of it. Personally I don't have a good answer to this question, but I think it may be that Elijah was in some sense testing Elisha's persistence. There is a Jewish tradition that when a person seeks to convert to Judaism, the rabbi is supposed to try to dissuade them three times and the person must insist three times that they wish to convert, because (according to the same tradition) becoming a Jew means taking on a very serious obligation, to follow the Law of God and live according to the ways of righteousness. It is a serious thing and is not supposed to be done lightly. I suspect that Elijah has a similar idea here, testing Elisha three times and telling him to stay and not follow the path of a prophet; not because Elisha is not anointed or not supposed to become a prophet, but because it is a hard and difficult path and Elisha should not do it if he is not completely committed.
Elijah himself is familiar with these difficulties, and we saw Elijah struggle intensely with depression from the stiff resistance he faced from both the people and the kings of Israel (see 1 Kings 19). Elisha should become a prophet, but should do so fully knowing how much it will cost him. Similarly, I think the companies of prophets may be trying to warn Elisha about the major changes that are about to begin in his life, and Elisha both knows and accepts those changes.
In verse 7, we see a group of 50 prophets come to witness Elijah and Elisha crossing the Jordan. My NIV study bible wisely points out that this group of 50 is likely intended to echo the 50 soldiers in the previous chapter that had come to capture Elijah. The reason being, while Ahaziah sent 50 men to resist Elijah, in this case God is sending 50 men to support him.
In verse 8, Elijah strikes the water with his mantle to divide it. In this book, Elijah's mantle is symbolic of his ministry and authority (and the ancient Jewish audience would have understood this reference). Back in 1 Kings 19:19, Elijah selected Elisha to be the next prophet by throwing his cloak upon Elisha. Here, Elijah uses his cloak (again a sign of his authority) to divide the water. Elisha's first act as a prophet is to perform the very same miracle, showing that the power and authority of Elijah was transferred to him. Moses divide the Red Sea and his disciple Joshua crossed the Jordan. Here, both Elijah and Elisha cross the Jordan to show God's favor upon them.
Crossing the Jordan also has symbolic value, representing the transition between eras. When Israel crossed the Jordan to enter Israel, they were leaving the time of wandering and entering a time of both conflict and tremendous blessing. In this chapter, crossing the Jordan is also symbolic of the transition between eras, as Elijah departs and Elisha arises to take his place as the LORD's representative on earth.
In verse 9, Elijah accepts Elisha as his successor; he is no longer seeking to dissuade Elisha, and simply asks what he wants. Elisha claims that he wants a double portion of Elijah's spirit, which is again a symbolic term. Asking for a double portion basically means that Elisha wants to be considered Elijah's firstborn with respect to Elijah's inheritance (see e.g. Deuteronomy 21:17). We saw this with Jacob giving a double portion to Joseph when Jacob claimed that both Ephraim and Manasseh would get a full portion of Jacob's inheritance, in effect giving Joseph twice as much as any other tribe.
Elijah once again warns Elisha that he is asking for a hard thing. This is a double entendre. Not only is it a hard thing for Elisha to inherit the full blessing of Elijah's ministry, it will also be a challenging calling that will test Elisha's endurance in many ways. It is both hard to get an anointing and authority of this kind, and also it is a hard life to live once you get it. Nevertheless, Elijah permits that Elisha may inherit his power and authority if Elisha remains so close to him and his pattern of living that Elisha would be present and would see him taken up into heaven. Elijah is demanding that Elisha should walk with him fully and that Elisha should behave in every way that Elijah does; in that case, Elijah's spirit would rest upon Elisha.
In verse 11, Elijah is taken up into heaven and departed the earth without dying. He is now the second (and last) person to do so, the first being Enoch (Genesis 5:24). I will talk more about this in a moment, but for now I want to finish the transition narrative since that is the principle theme of this chapter.
Elijah is taken up to heaven by a chariot and horsemen of fire, giving us a brief (and likely symbolic) view of God's heavenly power that had shepherded Elijah's life. Just as the 50 prophets demonstrate God's supremacy over the 50 soldiers of Ahaziah, the chariots of fire demonstrate God's supremacy over the chariots of human armies that typically dictated the flow of battle (for instance, the chariots of iron mentioned in Joshua 17:16 and Judges 1:19).
In verse 12, Elisha responds with "my father, my father, the chariots and horsemen of Israel!" This is also a double entendre. In one sense, Elisha is saying that his "father", Elijah, is the chariots and horsemen of Israel; that is, that Elijah was genuinely the power of Israel to help them defeat their enemies. Rashi supports this interpretation, by saying that Elijah benefited Israel more by his prayers than their chariots and horsemen did in battle. In another sense, Elisha is saying the chariots and horsemen of fire are the chariots of Israel, and that it is the power of God that fights on behalf of Israel to defeat their enemies.
Elisha tears his clothes in grief, but at this time there is nothing he can do to reverse what had happened. He is now prophet, and Elijah is taken from him by the will of God.
Elisha takes up Elijah's mantle and attempts to replicate Elijah's miracle: God does it, and thus Elisha is confirmed to be prophet with a company of witnesses. These witnesses want to go search for Elijah, which is peculiar because they (or their brethren) had earlier prophesied that Elijah would depart; Elisha also knows that Elijah will not be found, but becomes ashamed because the prophets may begin to think that Elisha (having taken Elijah's ministry) does not want Elijah to be found. So he permits them to go, but gives them a very stern, "I told you so" when they are unsuccessful. Why would the prophets insist that they should look for Elijah? Rashi suggests that "the holy spirit departed from the prophets" on the day that Elijah was taken away, though personally I don't think there is a whole lot of textual support for that position.
Having performed one miracle, Elisha almost immediately begins a string of miracles that span the next several chapters. The first one (after crossing the Jordan) is to heal some "bad water". The nature of the badness is not specified. Interestingly, Elisha responds by throwing salt into the water. Considering salt water is undrinkable, this is a peculiar ritual, but it has an interesting explanation. It is possible that the salt here is intended to represent the covenant with God, since salt is used symbolically in several places (see Leviticus 2:13 and Numbers 18:19). We don't know exactly what this term entails or if there is a particular covenantal salt ritual, but the language makes it clear that salt is somehow related to the notion of covenants generally and is used at least once to refer specifically to the covenant between God and Israel.
It is the covenant, or at least a reminder of the covenant, that heals the water and makes the land productive, reversing the curse that befell Israel when they joined themselves with idols and broke the covenant with God. So Elisha is healing the water at the same time that he is in a sense rebuking the people for turning away from God. He is reminding them that if they return to the covenant of salt with God then God would heal their land and their divided nation.
Lastly, Elisha goes from the Jordan river up to Bethel, which was one of the two towns with a golden calf and a center of idolatrous worship in the northern kingdom Israel, though it is also a home to one of the companies of prophets (which we saw earlier in this chapter). On his way up, a group of young men come out to mock him saying "go on up, you bald head!" Elisha responds by cursing them so that two bears come and kill a bunch of them. My first reaction (probably everyone's first reaction) is that this seems like a massive overreaction on Elisha's part. Some young kids come out and call you a bald head (which is a weird insult to begin with) and you think the best thing you can do is have some bears come and kill 42 of them. That seems way out of proportion with what Elisha was subjected to.
I have several thoughts about this short but strange passage. First, this is a critical transition period and Elisha needs to establish his authority. I think this is an important point so I will belabor it. Every time there is a transition in God's leadership of his kingdom, it is very important early on to establish the authority and authenticity of that new leadership, as well as the tone of that leadership. For instance, consider the story of Rehoboam when he became king at the death of Solomon (1 Kings 12). In that case, the people go and ask Rehoboam to lighten their burden, and Rehoboam responds by implying that he would increase their burden. He was attempting to establish a precedent that he would rule over them harshly, so they rebel. In this chapter, the youth of Bethel are establishing a precedent that they would not respect and would challenge God's prophet, and if Elisha permitted that to be done at the beginning of his ministry, then nobody would ever respect him.
Elisha is not just some random guy. He literally just divided a river with his cloak; being the prophet of God is pretty serious. Remember when the elders of Bethlehem trembled at the arrival of Samuel (1 Samuel 16:4)? They asked him if he came in peace because they knew that Samuel had the authority of God and the power to destroy them by his pronouncements. Without that power, Samuel would not have been able to influence the nation and turn them (to what extent he did) towards God. This is important because neither Samuel nor Elisha have the power of the army; they cannot compel anyone to do anything by force of arms. Indeed, it was the army that Ahaziah sent to apprehend Elijah contrary to God's will. Instead, it is the power of the chariots and horses of fire (the power of God) that stands behind Elisha and this must be a power even greater than the power of swords and bows.
Second, the youth are part of the idolatrous system. Even though they are young, they are harassing Elisha because they are in opposition to everything he stands for. This is not a random event: they are specifically insulting Elisha because of his prophetic ministry.
Third, calling him a bald head is indeed an insult. "Bald head" is intended to suggest that Elisha lacked power or physical prowess (for instance, see 2 Samuel 14:26 regarding Absalom's excessive hair).
Fourth, although Elisha may have understood that God would kill some of the youth, he doesn't specifically call for the LORD to do so. God does it of his own power because of the seriousness of this situation and the need to establish Elisha's authority as a prophet to the whole nation.
Lastly, "go on up" is yet another double entendre. In one sense, the youth are telling Elisha that he should "go on up" to Bethel, but in another sense they may be telling him to "go on up" to heaven like his master Elijah and depart from their country. In that sense, they are again mocking him by despising even God's miracle when he took Elijah away to heaven.