In Beowulf, the battle with Grendel is set at Heorot, the royal hall of Hrothgar, the Danish king. Prior to Beowulf's encounter with Grendel, the monster had engaged in regular pillaging of Heorot for a considerable length of time (about twelve years, in fact), and he wreaked considerable havoc on Hrothgar's subjects by violently devouring many of them.
The fact that Beowulf fights and defeats Grendel at Heorot is significant. Heorot can be seen to represent civilized order in the midst of wilderness, while Grendel can be seen as the chaotic force attempting to topple said civilization. As such, the fact that Beowulf defeats Grendel at Heorot signifies the return of established order in the face of chaos and disorder. Of course, Beowulf's efforts have only begun after his defeat of Grendel (he still has to face Grendel's mother and the dragon), but his battle at Heorot is his first major victory in the epic.