Why does Beowulf travel to the land of the Danes?

Beowulf travels to the land of the Danes, Hrothgar's land, because the stories of Grendel's attacks have spread.  Grendel has been attacking Heorot for 12 years and so the word has reached the land of the Geats - Beowulf's land.  Beowulf's father, Edgetho, had once fought alongside Hrothgar and Hrothgar had saved Edgetho.  Beowulf, therefore, feels somewhat in debt to Hrothgar.  This information comes to light when Beowulf arrives in the land of the Danes (approximately ll. 185-285). He also tells Unferth and some of the other Danes who are less thrilled to see Beowulf arrive that the Danes don't seem to be fighting back for themselves. Later, we find out that Beowulf wanted to make a name for himself so fighting and defeating a monster like Grendel would fulfill that.