his life to face Grendel in battle.

Beowulf emphasizes the worth and nobility of Heorot, the mead hall. He refers to Hrothgar as a good king, because of the protection and hospitality he shows warriors. He frames possibly sacrificing his life as a favor to be granted.

Although Beowulf has great confidence he can win, he ends the speech stating that the outcome is up to God, showing his humility.

The speech characterizes Beowulf as an exemplary man in his society. Not only does he have the traits his culture most values—bravery and great strength, both of which keep people safe from outside threats—but he also is civilized. This is the key trait that differentiates him from Grendel, who is also brave and strong. Beowulf's courtliness and respect toward both Hrothgar and God show his adherence to the social order and social norms. Grendel, in contrast, shows his evil nature in his contemptuous disregard for human culture and malicious pleasure in upsetting it.

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. 

One piece of characterization that encompasses some of the elements in the previous post is Beowulf's enormous ego and bragging speach.  Modern audiences are sometimes put off by this bahvior because we tend to value a humble attitude, but in the Anglo-Saxon culture, reputation for bravery and skill in battle were vital to life, so Beowulf's listing of his past accomplishments and his determination to fight alone and without a weapon are part of this culture.  He doesn't play coy; he directly states that he has accomplished many great deeds and goes on to list them.  This kind of talk was meant to both intimidate foes and reassure the people -- they learn first hand what Beowulf thinks he can accomplish, and stay tuned to see if he can deliver what he promises.

What you are asking about is characterization.  What characterization is accomplished by Beowulf's speech?

First, we learn that Beowulf has a sense of duty:

My people have said, the wisest, most knowing
And best of them, that my duty was to go to the Danes'
Great king.

The mead hall is plagued by Grendel, and Beowulf feels it is his duty to come help. 

We also learn that Beowulf has performed great deeds:  rising out of the darkness of war covered in his enemies' blood, chaining five giants, etc.  His deeds are his testament, his demonstration of worthiness.

Beowulf also believes in fate, at least when he is using rhetoric in the form of a speech:

...Now Grendel and I are called
Together, and I've come. 

His battle with Grendel is his destiny, his fate.

Beowulf is also independent--he requests to fight Grendel by himself--and honorable--he will use no weapon, because Grendel uses no weapon. 

Finally, Beowulf puts himself into God's hands.  He leaves it up to God to determine the outcome of the battle. 

Scholars assume that these personality traits and beliefs were important to Anglo-Saxons, in general.  Beowulf is probably the ideal Anglo-Saxon hero.

Line numbers sometimes differ, so I'm taking a chance on this--I hope that the speech to which you refer is the speech he makes to the Danes and their nobility:

When we crossed the sea, my comrades and I, I already knew that all my purpose was this:  to win the good will of your people or die in battle, pressed in Grendel's fierce grip.  Let me live in greatness and courage, or here in this hall welcome my death!

From this, we know that Beowulf is brave, boastful, confident, and resolved to be victorious or die.  He is a good leader, or the men he brought with him would not have come. His brave words give Hrothgar and his wife, Welthow, encouragement and hope for the future of their land.

First, it is obvious that Beowulf is very gracious.  He flatters Hrothgar and his mead hall, Heorot, calling it the "best of all mead-halls". He also shows that he is one who is unafraid to help, telling Hrothgar that when it was suggested to Beowulf by his people that he help the Danish people rid themselves of Grendel, he accepted the duty.  He tells Hrothgar that he was chosen because of his strength and fierceness in battle so that tells the reader that Beowulf is a good warrior.  He goes on to tell Hrothgar about a battle he had with five great giants and how he was victorious.  This shows that he possesses a strength beyond normal.  Next he tells Hrothgar that he will fight Grendel with no weapons but his own hands because Grendel uses no other weapons and it wouldn't be a fair fight otherwise.  This shows that Beowulf is very courageous.  Finally he says that the outcome of the battle is in God's hands and he is content with that.  This reveals Beowulf's devotion to God.