Beowulf, a noble warrior in the prime of his life and the nephew of Hygelac, the king of the Geats, hears about Grendel. With fourteen loyal men, Beowulf sails to the land of the Danes.
Beowulf sails to help the Spear-Danes because he's a warrior and seeks to do great deeds and win fame.
When the Geats arrive in the land of the Danes, a watchman at the sea-cliff challenges them. He asks where they're from, what their lineage is, and why they have come. From Beowulf's stature alone the watchman can tell his is a mighty warrior.
Note that the watchman doesn't ask who they are, but for their lineage (tribe and family). Family, in this culture, is the measure of a man.
Beowulf says the warriors with him are Geats, loyal warriors of king Hygelac. Without giving his name, Beowulf identifies himself as the son of Ecgtheow, a man Hrothgar the son of Healfdene knows. Beowulf says the Geats, having heard of Grendel's attacks, offer help. The watchman lets them pass.
The connection between Ecgtheow and Hrothgar likely helps bring Beowulf to Heorot. Beowulf is returning Hrothgar's generosity to his father. Generosity wins loyalty.
At Heorot, Hrothgar's herald, Wulfgar, asks the Geats who they are. Beowulf identifies himself by name as well as by his service to Hygelac, and asks to speak to Hrothgar. Wulfgar brings this request to Hrothgar.
This is the first time Beowulf identifies himself by name. Up until this point he had named only his tribe and his father.
Hrothgar corroborates that he knew Ecgtheow, and adds that he knew Beowulf as a boy. Hrothgar mentions that Beowulf's grasp is supposedly equal to that of thirty men, and concludes that God must have sent this warrior to help the Danes.
Though a pagan, Hrothgar here credits God for bringing Beowulf. The scribes' attempt to make the poem Christian isn't always clean.
Wulfgar invites the Geats to speak to Hrothgar. Beowulf greets Hrothgar, and says he has heard that because of Grendel, Heorot stands empty and useless after nightfall. Beowulf boasts of the great deeds of his past, saying he bound five others in a fight, destroyed a family of giants, and vanquished water-monsters. Now he comes to fight Grendel.
Through boasting, a warrior emphasizes his daring and skill to win fame. A good boast shows intelligence and quick wit, though it won't reflect well on the boaster if he can't back up his words with deeds.
Because Grendel does not use weapons, Beowulf says that he will fight Grendel with his bare hands and if he loses, they won't have to bury him because Grendel will carry his body away to eat it. He asks only that his mail shirt, the work of Weland the Smith, be returned to Hygelac. Beowulf concludes with the statement "Fate will go as it must."
Giving up weapons shows how little Beowulf fears death in his quest for fame and great deeds. Also note his reference to fate, a pagan idea.
Hrothgar responds, saying that Ecgtheow, Beowulf's father, sought sanctuary with Hrothgar after Ecgtheow killed Heatholaf of the Wylfings. Hrothgar purchased peace from the Wylfings with treasure, and Ecgtheow swore an oath of loyalty to Hrothgar.
Loyalty is passed down from father to son. Note also how treasure functions as a diplomatic tool.
Hrothgar accepts Beowulf's offer, though he adds that he has often heard his men boast while drinking that they would meet Grendel with their swords in Heorot, only to find the hall awash in their blood the next morning.
Here Hrothgar describes bad warriors. The implication is that they not only die, but die in shame for failing to live up to their boasts.