What do we learn about Beowulf's character from his speech in lines 365-405 of Beowulf?
One of the most important elements of the exchange among Wulfgar, Hrothgar, and Beowulf is not in what is said about Beowulf but in what is alluded to by Hrothgar. An obvious purpose of this section, of course, is to introduce Beowulf formally to the man he has come to serve, Hrothgar, and, beginning in line 405, for Beowulf to set forth his tribal allegiance and his qualifications for the task of ridding Hrothgar of Grendel.
Hrothgar begins his speech, however, with a comment that, as we learn later, establishes the basis for a familial relationship between Hrothgar and Beowulf. This is a bond that draws the two men into a much closer relationship even than a retainer's allegiance to his king:
I knew [Beowulf] when he was a boy; / his aged father was called Ecgtheow, / . . . has his offspring now boldly come here, sought a kind friend? (ll. 372-376)
Hrothgar alludes to a very important event involving Beowulf's father, in which Ecgtheow, who has killed a man of another tribe and is unable to pay compensation for the killing, flees to Hrothgar's court for protection. Hrothgar not only takes Ecgtheow in and protects him from retribution but also pays the wergild (the man-price or compensation) to the murdered man's family, which settles the dispute between families and, more important, between tribes.
Because of Hrothgar's relationship with Ecgtheow, Beowulf's father, Hrothgar and Beowulf are heirs to a personal and familial relationship that transcends a retainer-king relationship. When Hrothgar refers to himself as a "kind friend" rather than simply a king or leader of the Danes, he is subtly pointing to the "blood" relationship that exists between himself and Beowulf.
Beowulf does not actually speak until line 405 in the Old English text. Instead, we have a speech by Wulfgar introducing him.
The section comprising lines 365 to 405 begins with a speech by Wulfgar. He describes Beowulf and his band as having high-quality armor, suggesting that they are wealthy and expert warriors. He then mentions that Beowulf himself is reputed to be as strong as 30 ordinary men, has an excellent reputation as a warrior, and is also devout and of good character. He also mentions that Beowulf is the son of Ecgtheow and that Wulfgar met Beowulf when Beowulf was quite young. Wulfgar thinks that Beowulf will be a valuable ally against Grendel. We discover that Hrothgar already knows of Beowulf and welcomes him.
Beowulf, in his speech beginning at line 405, boasts of his previous deeds and offers his help in slaying Grendel. We also discover that he takes honor and family obligations seriously.
Lines 365 through 405, of Beowulf, contain Wulfgar's request (and Hrothgar's response) to Hrothgar regarding the acceptance of Beowulf's help rid Heorot of Grendel. Beowulf does not actually speak until line 407 when he hails Hrothgar and begins to tell him about his (Beowulf's) renowned history.
Therefore, the lines in question tell of Beowulf's character, but not through Beowulf's own dialogue. Readers do find out that Wulfgar greatly respects Beowulf. He tells Hrothgar that Beowulf is worthy, noble, and powerful. Hrothgar then tells Wulfgar that he has heard of Beowulf and had helped Beowulf's father (Ecgtheow) at one time. Hrothgar readily accepts Beowulf's help.
Wulfgar returns to Beowulf and tells him of Hrothgar's acceptance of him. Wulfgar also tells Beowulf that Hrothgar has heard of his strength and accomplishments. In line 405, Beowulf is being described as beginning to speak to Hrothgar.