In this chapter, Samuel ministers before the LORD while the sons of Eli do evil.
This chapter begins with the song of Hannah, whose primary theme seems to be the reversal of fortunes between those who are strong and those who are weak. The proud are humbled before the LORD, while the barren woman (Hannah herself) "gives birth to seven [sons]". Seven, as before, is the number of completion or fullness, so this metaphorically indicates the completion of the barren woman's restoration to favor. While much of the song is devoted to showing that the LORD controls the fortune of all persons and can make the rich become poor, or the poor become rich, she concludes by stating the pattern underlying this behavior: the LORD "keeps the feet of his godly ones, but the wicked ones are silenced in darkness." In his strength and power, the LORD judges men by their righteousness.
Verse 10 contains an interesting admission: "he will give strength to his king." Which king does this refer to, since there is no king over Israel at this time? I say this ironically. This verse is probably a slight anachronism, referring to the king who would shortly emerge over Israel. Indeed, Samuel himself will anoint this king, so Hannah actually plays a role bringing about the kingdom that she anticipates in her song.
Verse 12 tells us that the sons of Eli were literally "the sons of Belial; they did not know the LORD". Belial is one of the idolatrous gods of Canaan. It tells us that the priest's servant would take a piece of meat from each offering while the fat was still on it. If the person offering the sacrifice complained, they would threaten violence until their demands were met.
Taking meat from the offerings is not a sin. In fact, this is how the priests would make a living. Certain kinds of offerings had to be completely burnt, but most offerings only required a small portion to be burned, always including the fat from the animal. The rest of the meat would sometimes be eaten by the petitioner (in the case of a fellowship offering), but in most cases would be given to the priest. In all cases, eating the fat was a grave sin and is prohibited several times (see e.g. Lev 3:17: "you shall not eat any fat or any blood", or Lev 7:22-27, which says the same thing in more detail). Verse 17 tells us that their sin was very great, and Leviticus explains in more detail how their behavior was sinful. As priests, they should be intimately aware of the Law's regulations governing animal sacrifice, so they don't really have any excuses. If my readers want to learn more about how the Law of Moses governed animal sacrifices, I encourage them to read Leviticus chapters 1-7, which I have previously covered in my commentary (beginning here).
Samuel, on the other hand, is ministering before the LORD in a linen ephod (the priestly garment). As I said when discussing the previous chapter, Samuel is an Ephraimite, but ministering before the LORD as if he were a Levite. On the other hand, the sons of Eli are called "sons of Belial", even though biologically they are sons of Levi and have the right to minister in the Tabernacle.
Hannah, for her part, is blessed by the LORD and gives birth to 5 more children. This is the last we ever hear about Hannah, but we can rest assured that the LORD "visited" her and she has what we can only presume is a blessed life of one sort or another.
On the other hand, it appears the sinfulness of the sons of Eli continue, as they also have sex with the "women who served at the doorway of the Tent of Meeting". I would guess these are Levite women, but there wasn't any place in the Law of Moses that their service is stipulated. Polygamy is not against the Law (indeed, Elkanah himself came to the Tabernacle with two wives), but we can easily hypothesize that the behavior of Eli's sons constituted adultery or prostitution or some form of sexual immorality. Maybe they used their positions of power to coerce the women into sex? The text doesn't really say, but it's evidently bad.
Eli rebukes his sons. but evidently he does not do enough to stop them. He "honors [his] sons above me". An anonymous "man of God" comes to deliver a rebuke to Eli, promising that his family will perish even while the LORD is doing good for Israel at large. The LORD will raise up a faithful priest (Samuel), "and he will walk before my anointed one always". The "anointed" is a reference to the future king, whom Samuel himself with anoint with oil as a symbol of the LORD's favor.
If there's one big point to this chapter, it's to draw a contrast between the sinfulness of Eli's sons. the next generation of priests being raised up, and the faithfulness of Samuel. Samuel is "adopted", in the sense that he comes from another tribe, while the sons of Eli are descendants of Aaron but nevertheless do a lot of wrong stuff. This reminds me of Jacob and Esau. Esau was by right the elder son, but Jacob became the son of the promise, the father of the nation that inherited the promised land. Similarly, Ephraim was younger than Manasseh, but Ephraim was blessed by Jacob to be greater than his brother (Gen 48:13-20). In this case it is Samuel, the outsider, who is righteous, while the natural-born Levites are sinning in the LORD's presence.
I called it a "paradox" that Samuel gets to serve with the Levites. This chapter shows us that Samuel is more righteous than the men born into the priestly service, and in a way that is a second paradox. Like in Hannah's song, the men who were born into power and influence in the priestly service are going to be thrown down, while Samuel who is born as an Ephraimite will "walk before my anointed one always". This is a second, and more subtle, fulfillment of Hannah's song. It doesn't matter what family you are born into, if you honor the LORD, the LORD will honor you (v. 30). The LORD cares more about faithfulness and righteousness than having the right ancestors. It was kind of the same way with Ruth, who was born a Moabite, but adopted into Israel because of her faithfulness to Naomi and righteousness before the LORD.