Beowulf, a young Geatish warrior, fights Grendel unarmored and with his bare hands, using raw strength to rip off Grendel's arm. He does this as a point of honor because Grendel fights without weapons, and Beowulf thinks it is wrong to take unfair advantage.
Beowulf is apparently not aware that Grendel cannot be harmed with weapons, as is shown by the fact that his men can't even scratch the monster. This narrative point indicates how Beowulf's sense of honor ensures he does not make a critical mistake. It may also be interpreted as an indication that Beowulf chose the correct weapon. He fights a primal force, Grendel, with the most primal of human weapons, brute force.
If the poem is read on an allegorical level, Grendel, the descendant of Cain, is the very embodiment of evil, possibly the evil within mankind. By fighting him directly with no weapons, Beowulf uses not physical strength but moral will to defeat the evil in himself, symbolically ridding himself of the mark of Cain and showing himself to be a true hero worthy of fighting greater monsters such as Grendel's mother. This reading is reinforced by King Hrothgar's later speech crediting Beowulf's victory to God as well as to the hero.