"Fin" is the Beaver and Steve equivalent of "The End" (The French are supposedly using it as well. What a bunch of copycats!). Since the early days, it tends to appear in a different and innovative way at the end of nearly every comic strip that isn't part of a continuous story.
It has even created a sort of a pseudo-religion around it, causing much uproar to emerge among the crowds when James sometimes forgets to add a "Fin" to a comic. On the other hand, he is more often generously rewarded for remembering to use one in yet another mind-blowingly cunning manner.