An epic hero is, in short, the hero of an epic. An epic is a story, usually a poem, where a character goes on a quest. There are some characteristics that an epic hero often has. You can read about them in my first link. Here are some ways Beowulf is an epic hero.
(Please note that there are different versions of the poem. My quotes come from the enotes PDF. See my second link.)
Beowulf is a strong leader.
Beowulf is very persuasive and charismatic. He leads his men and they are honored to follow him. Sometimes the mark of a true epic hero is someone who can lead others and get them to go along with his will, and even follow him into danger.
Now many of Beowulf's band brandished ancestral blades, wanting to save the life of their leader, the proud prince, if such they could do. (ch 12,enotes pdf, p. 18)
Beowulf is clearly loved by his men, and they will follow him even into great danger. Beowulf provokes bravery in his men.
Beowulf has amazing physical prowess.
An epic hero is usually strong, often unusually so. Beowulf is strong enough to battle monsters with his bare hands, without a sword.
The monster desired to fling himself free, if at all he could, and fly far away to the fens—he knew that his fingers' power was in the grip of a fearsome foe; this was a dire march to Heorot that this devastating beast had made! (ch 11, p. 17)
Grendel doesn’t stand a chance! Beowulf’s strength leads to even more bravery, and makes others admire or fear him, depending on what side they are on!
His exploits are sung of and heralded.
Every good hero has to have a cheering section! All of Beowulf’s triumphs are sung, especially the defeat of Grendel.
Then gray-haired clansmen, many youths, and stalwart warriors rode back in high spirits on horses from the mere, and Beowulf's victory was recounted. Many a man said that among all the seas of the world, south or north, that none of the other shield-bearing warriors under the expanse of heaven's vault were more valiant or more worthy to rule! (ch 13, p. 19)
By recounting Beowulf’s glory over and over, he becomes a folk hero to all of the people. They admire him and love him for saving them.
The hero also gets gifts, of course. Often these are useful to him later.
Then did the son of Healfdene present to Beowulf a banner woven of gold as an ensign for the victory, an embroidered flag of battle, a helmet and a coat of mail, and a precious sword that was seen by many when they brought it before the hero. (ch 15, p. 21)
Beowulf gets a heroic sword to fight Gredel’s mother with.
The epic hero “dies” and is resurrected.
A significant part of the hero’s journey is where the hero is reborn. Beowulf kills Grendel, but then has to face and defeat Grendel’s mother. He does so by going deep under the dark waters, a symbolic death.
The life of the son of Ecgtheow, prince of the Geats, would have ended there underneath the wide earth if his armor of war, hard net of battle, had not aided him; and the Holy God, wisest Maker, wielded the victory. The heavenly Ruler championed his cause, and he soon stood on his feet again. (ch 22, p. 28)
So you can see that the epic hero is more than the sum of his parts. He is an inspiration to others.