What is going on in the Finn section (lines 1063-1250)?Why would this portion of the poem fall under the theme of "fame"?
Just after Beowulf kills Grendel, everyone in the kingdom gathers at Herot to celebrate around the trophy (Grendel's arm). During this time, people eat and drink and are entertained with song (by a man called a scop). His "songs" comes in the form of story telling, and at this time, he tells several old tales which are meant to compare or contrast with Beowulf's victory over Grendel. Ultimately, one point of these stories is to bring glory and honor to Beowulf by showing how he is most like previous (and still glorified) Danish heroes. Another point is to foreshadow future events. Finally, the brief history lesson of the stories is meant to remind the people of lessons they can learn from the past.
The "Finn esisode" is one of the stories told that night. It is a rather lengthy and confusing tale, but the general idea is this: a group of Danish warriors are visiting King Finn of Frisia because of an arranged marriage between him and the Danish King's sister. Likely, the two households are celebrating together, though the arranged marriage may signify the desire to end a feud. For reasons left unclear, the Frisians end up attacking the Danes that night in the place they sleep, and slaying most of them, including their king. In the attack, Finn's son is also killed. A truce is finally reached--out of necessity for the Danes--and the rest of the warriors remain in Frisia to wait out the winter. Before the men leave in the Spring, they avenge the death of their king by killing Finn, the king of the Frisians, and his men.
There are several meanings this story could hold for those celebrating Beowulf in the great hall of Herot that night. First, it reminds them of the virtue of loyalty and encouragement of revenge. Second, it foretells of potential danger that comes at a time of celebration. Just following this story, Queen Wealthow (Hrothgar's wife) makes a point to ask Beowulf to take care of her two sons should anything happen to Hrothgar.
As far as how this part of the story fits the theme of "fame," mainly this celebration evening is all about Beowulf and the retelling of his battle with Grendel. The audience can only assume that the mention of other such hero stories on the same night is to suggest that Beowulf's story will later be told in the same way.