Beowulf is an Anglo-Saxon epic poem; its hero is Beowulf and one of Beowulf's victories in this story is killing Grendel. Since there are many translations of this poem into English, the exact wording of any quoted lines may be a little different than the translation you are reading, but the sense is the same.
Grendel is described as the "monster of evil," the "devil from hell," the "direful demon," and the "horrible stranger." He is descended from the line of Cain, who was punished by God for killing Abel, his brother. Grendel and all monsters in general are descendants of Cain and have been cursed by God. Grendel has been relegated to "the land of the giants" and other "ill-favored creatures" who "grappled with God." Specifically, Grendel lives in a swampy, smelly fens on the moor.
Grendel "nursed a hard grudge" against King Hrothgar, and every meal and merriment that happened in Heorot, Hrothgar's mead-hall, infuriated Grendel. We do not really know the specific cause, but we do know how he reacted. "Since God did oppose him, not the throne could he touch"; however, Grendel could kill people, and he did--often.
Hrothgar is unable to defeat Grendel, but Beowulf hears of his plight and comes to kill Grendel. We do not have much of a physical description, but Grendel is strong and has some version of a pouch; in one battle, Grendel carries off thirty grown men (at one time) before eating them. One night Grendel attacks and is surprised to find someone ready to fight him. Beowulf is said to have the strength of thirty men in each arm, and Grendel fights Beowulf valiantly, hand to hand, until Grendel's arm (which is really looks more like a claw) is wrenched out of its socket.
The defeated Grendel slinks home to his fen to die. Later, Beowulf defeats Grendel's mother and triumphantly brings Grendel's head back to Hrothgar; it is so large and heavy that it takes three men to carry it on a pike from the ocean to the mead-hall.