I began a sermon series on the book of Samuel yesterday, going through 2:11 to start. Here's the outline:
I. 1-8: Hannah’s barrenness
II. 9-11: Hannah’s prayer
III. 12-18: Eli and Hannah
IV. 1:19-23: Birth of Samuel
III. 1:24-28: Eli and Hannah again
II. 2:1-10: Hannah’s song
I. 2:11: Hannah’s fruit
Notice the symmetry. It's called a chiasm, in the scholarly world. I prefer the "sandwich theory," because it's what's in the middle that defines a sandwich - so also it is what is in the middle section that is key. Here it is God remembering Hannah and the birth of Samuel.
Some extra stuff that didn't make it into the (already too long!) sermon:
1. The text hints that Eli is less than faithful in his sitting in the temple and assuming Hannah is drunk. The language in verse 12 highlights this. The word used for Hannah praying is "intercede," "mediate," "arbitrate." This is what Eli was supposed to be doing. But what is he doing? He is watching Hannah! And Hannah is interceding "before the face of Yahweh" which is the exact language for what a priest was supposed to do. I suppose this makes the argument for some liberal friends that women ought to be allowed to be ministers. But I'd say instead that it foreshadows Hannah's child (she prays for a boy), who will intercede that way, and that it contrasts with what Eli should be doing.
2. The effect of prayer on our spiritual condition: verse 18. After she prays and is blessed by the not-utterly-corrupt Eli, she eats and is not sad. She is already comforted, even before knowing if she will receive what she asked for. This is like the Psalms, where the Psalmist is in distress, prays, and then gives thanks right away. Nothing has happened yet - except the most important thing of pouring out one's heart before Yahweh.