Why does Beowulf journey across the sea to the land of the Danes?

Beowulf travels from his own home in Geatland to that of the Danes because of the terror that the monster Grendel has brought upon that land. Grendel had wreaked havoc upon the Danes for twelve years before Beowulf arrives. Beowulf has a previous reputation of being a hero in his own land, so the king of the Danes, Hrothgar, asks him to come. It is in the battle between Grendel and Beowulf that the reader is able to see the monumental forces these two characters are meant to represent. Grendel is described as a descendant of Cain and the bloodthirsty epitome of evil, being a monster who enchants his body to withstand blades. In response, Beowulf, does not attempt to use a weapon but rather is able to tear Grendel's arm off, thereby fatally wounding him, with his bare hands. Essentially, Beowulf is meant to be seen as the only person capable of slaying such a great foe.

At the beginning of the epic, the king of the Danes, Hrothgar, is plagued by the ferocious monster Grendel, who stalks Heorot at night and has killed numerous brave Danish warriors. For twelve years, Grendel has terrorized the mead-hall until Hrothgar remembers Beowulf, the hero from Geatland, and requests his help defeating Grendel. Beowulf ends up sailing from Geatland with fourteen of his bravest warriors and vows to kill Grendel. Hrothgar had once helped end a feud between Beowulf's father, Edgetho, and the Wulfings years ago and views Beowulf's service as repayment for helping Edgetho. Shortly after Beowulf arrives in Denmark, he ends up defeating Grendel in the great mead-hall by fatally wounded him in their epic struggle. Beowulf manages to rip Grendel's shoulder, arm, and claw from his body before the monster flees back to his mother's lair, where he eventually dies.