The story of Finn, as told in Beowulf, is important given the contrast the story sets up. Prior to the telling of Finn's story, the story of Siegmund is told. Siegmund is a very positive story and is used to compare Beowulf to a great man.
In contrast, the story of Finn is meant to be one of a warning. The use of the story warns against one being a bad ruler. Unlike Siegmund and Beowulf, Finn is killed by the Danes for his unacceptable behaviors and actions.
Therefore, the purpose of the story is to warn others about the consequences of not being a true hero. If one is a true hero, they are raised up and celebrated by those around them. On the other hand, men who treat their followers badly will suffer for the mistreatment.