In this chapter, Jacob is sent out of the promised land and encounters God for the first (recorded) time.
When I think of the story of Abraham, the central theme I see is faith. He goes out to an unknown land, trusts God and is willing to sacrifice his son all by faith. He is breaking new ground and establishes the Abrahamic faith.
When I think of the story of Jacob, what I see is a man who grows out of an early sin pattern, deception, passes through a series of challenges, and ultimately overcomes to establish his identity.
When Jacob was born, he was grasping his brother's heel. This is his sin pattern: deception. His father had a promise to inherit the land, but this promise was not shared with Jacob and by everything we had seen, his father was going to pass it on to his eldest son, Esau. But Jacob falls into his sin pattern and steals his brother's blessing to supplant him, as his name suggests he would do. Yet, as a result of this sin pattern, he is forced to leave the land that he would otherwise inherit (though, again, he does not know about the promise). This is directly contrary to the command given to Isaac, so it's pretty clear that this is a metaphorical departure from his destiny. His destiny lies in the promised land, not in Chaldea. So he is being sidetracked by the force of his sin pattern from the goals in his life.
In this chapter, the first thing that happens is he is sent away. I find it interesting that Isaac does not actually address Jacob's deception. It is strange to me that he does not mention it at all, and acts like Jacob never did anything. I don't know why this is.
Another thing we see in this chapter (and the end of the prior chapter) is the awkwardness of marrying the local Canaanite women. It is a point of difficulty for Rebekah when Esau marries two Canaanites. So even before it is explicitly condemned by Moses, the early Hebrews are already struggling with the issues related to intermarriage. Esau tries to "fix" the issue by marrying one of Isaac's relatives, which is a questionable decision with a largely undocumented outcome (that is, the Bible doesn't state how this affected his relations with his parents).
Then Jacob has a dream.
First, note the contents of the dream. It speaks specifically about a "ladder" that rises from the earth whose top reached into the heavens. There are angels ascending and descending upon the ladder, and at the top of the ladder stands the Lord. I will address this in more detail later.
Second, note the contents of the Lord's message, which is shared while Jacob is still in the dream. As with Isaac, the Lord is largely recapitulating earlier promises made to Abraham and Isaac. In particular, that his "descendants will be like the dust of the earth", that he would possess the land, and that in him and his descendants "all the families of the earth will be blessed" (Gen 12:3). He adds one more relevant detail, which is that the Lord promises to bring Jacob back into this promised land and will protect and keep him wherever he goes. So unlike the Lord's earlier command for Isaac to remain in the promised land, this time the Lord seems to accept and understand Jacob's need to leave and promises to be with him regardless of where he goes. This reminds me of Jesus's promise in Matthew 28:20 where he says "I am with you always, even unto the end of the age".
The third and last element I will address is Jacob's response. His first response is fear, but later he sets up the very stone that he put his head on as an altar of sorts. Then he makes a pledge of service to the Lord. I will address this last.
The contents of the dream have several predicates and several conclusions. One of the most important predicates and the only one I will discuss is the nature of angels. The Hebrew word for angel transliterates to malakh which primarily means messenger or ambassador, in the sense of "delivering a message" with a secondary sense of "spreading the influence of an authoritative sender". "Angels of God" are therefore messengers or servants of God who are responsible for spreading his influence, sharing messages with given recipients, or generally influencing the world in accordance with the desires of their master.
They are only supernatural/spiritual implicitly, as one can learn by reading the context of passages that speak of angels. There is also the more specific term "angel (singular) of the Lord" whose interpretation is somewhat more ambiguous. The angel of the Lord is sometimes considered a "traditional" angel but also sometimes considered either a physical manifestation of the Lord himself or possibly even a metaphorical term for the influence of God in a general sense. If anyone is surprised by the concept of the Lord manifesting physically, just re-read Genesis 3:8-9.
That said, what we can conclude from angels traveling along this ladder is the direct connection between heaven and earth, with a sense of God's continuous divine influence and impartation upon the earth, both in terms of effecting change but also in terms of sharing messages from the Lord for specific people. Also significant is the ascension of angels from the earth to the heavens, which can either represent angels returning from missions to the earth or also can signify angels bearing messages from humans directed to God.
This brings up my next point: the inherent accessibility of God. Since there is a ladder connecting earth (people) to heaven (God), God is inherently accessible to mankind for intercession or communion. If we remember back to Genesis 2, there was an inherent unity between man and God which existed in the Garden of Eden. God interacted with man and spoke with him regularly. Yet this unity was destroyed by sin and the fall from grace which occurred in chapter 3, and while God is still described as speaking directly to Cain in chapter 4, from chapter 5 and onward the described interaction between man and God minimized rapidly. Beginning with Abraham, there is a reconnection between man and God, yet it is a tenuous reconnection that is chiefly characterized by brief (yet potent) interactions where the Lord shares a specific message and then.... that's it. There is no sense of the mutually abiding presence of man and God, with one possible exception when the Lord and the two angels visit Abraham before going on to Sodom and Gomorrah. Yet here, in this dream, we are shown a permanent structure which binds the divine with the mortal, the dust of the earth with the stars of the heavens, with messages passing up from man to God and down from God to man.
Regarding Jacob's response to this dream, I have heard a number of teachers share various things about this passage, and it seems that a lot of people are critical of Jacob's response. In particular, there is sometimes a comparison drawn between Jacob's "conditional tithe" and Abraham's "unconditional tithe". In particular, some teachers assert that Jacob is trying to draw up some sort of bargain with God, which they similarly assert is a bad thing, that one cannot deal with God nor should one try.
Personally, I don't think these arguments hold a lot of weight for one main reason, which is that they do not seem to account for the culture that Jacob is operating in. Among other things, just look at the life of Abraham himself, in chapter 15. After Abraham asks for assurances regarding God's promise, God initiates a covenant ceremony with him. And then later, Abraham negotiates with God regarding saving the righteous from Sodom, which I just talked about! So it perplexes me why people think these things are okay for Abraham but bad for Jacob. As for Jacob's conditions, from what I've seen this is a fairly conventional suzerainty-vassal agreement where in exchange for protection and provision, Jacob would serve the Lord and give him tribute. To say that Jacob is trying to "manipulate" God based on this is misleading at best.
My opinion about this passage is that we are seeing exactly what it looks like: Jacob just met God for the first time and he was scared by it. He knew about God from the teachings of his father Isaac and the traditions of his family going back to Abraham, but now he met the God he had only heard about before. He did what any reasonable person would do, which is agree to serve God as his lord. The only issue is that this form of vassal-lord treaties does not exist in modern life, so some people misinterpret it for that reason.
I also think it's reasonable to draw a parallel with Abraham's tithe, but it's not a negative "Abraham good, Jacob bad" thing, it's more of a "Abraham and Jacob both offered tithes to God and the similarities are surprising" thing.
So remember the story I shared about Jacob at the start? He was driven out of his promised land, but now he has the promised protection of God, he is given the promise of Abraham by God (v. 13-15) and is now the carrier of that promise for real, and he establishes a covenant to serve God much like Abraham did.