Part of this answer depends on what your definition of a hero is. Plenty of people say that their mom or dad is their hero, but those people rarely fit the stereotypical Hollywood media definition and image of a hero. Beowulf shares many characteristics with modern day heroes such as Captain America, Thor, and Batman.

First, Beowulf is strong. His strength isn't hidden either. He looks like a powerfully built warrior type person. Early in the poem, Beowulf is on his way to meet Hrothgar. A guard stops Beowulf, and the guard demands to know what Beowulf is up to. Beowulf must present an inspiring image because the guard comments on Beowulf's heroic looking image:

Nor have I seen

A mightier man-at-arms on this earth

Than the one standing here: unless I am mistaken,

He is truly noble. This is no mere

Hanger-on in a hero’s armour.

If you need further evidence of Beowulf's actual strength, the following quote works quite nicely:

Who valuable gift-gems of the Geatmen carried

As peace-offering thither, that he thirty men’s grapple

Has in his hand, the hero-in-battle.

Finally, keep in mind that Beowulf is strong enough to literally rip Grendel's arms off.

Like other stereotypical heroes, Beowulf is brave. Grendel is a scary, demon possessed monster that eats humans. Along with that bravery is the fact that Beowulf intentionally seeks the danger out. That is an important hero characteristic. It's not seen quite as heroic to fight for your life when you have no other options; however, intentionally seeking out danger in order to protect others is definitely heroic. From firefighters to Thor, those heroes run toward danger. Beowulf does the same thing. He chooses to fight Grendel.

A third heroic quality of Grendel is that he is humble. He is definitely confident in his abilities, and he might brag a bit about his battle prowess; however, he doesn't abuse his hero status. He is offered the Danish throne and riches beyond his imagination for his heroism, yet Beowulf turns it down. He returns to his land the same way that he left it, and that is very common for media heroes. Spider-Man goes back to being picked on as Peter Parker, the Incredibles go to Dash's track meet, and Shrek returns to his swamp.

Beowulf has many qualities that make him a hero. Two major ones for his role as this sort of hero are his bravery and his fighting prowess. In other words, he is brave and a powerful fighter.

His major defining actions are directly related to these qualities. He is willing to fight Grendel, and then to fight Grendel's mother, even though fighting the monster's mother means going into a cavern by himself.

Much later in life, he's willing to go fight the dragon. This might be his greatest act. Beowulf knows that he is old, and not nearly as strong as he used to be. However, because the dragon is threatening his people, he goes to fight it, even though he dies as a result. This shows that his virtue is even greater than his physical power.