At the climax of his battle with Grendel, Beowulf tears the monster's arm off. Remember, Beowulf has the strength of thirty men in each arm which is why he is able to rip off the beast's limb. Grendel's arm is displayed in the mead-hall as a trophy. It symbolizes the triumph over Grendel and his reign of terror:

And although he got away
to enjoy life's sweetness for a while longer,
his right hand stayed behind him in Heorot,
evidence of his miserable overthrow
as he dived into the murk on the mere bottom. (2096-2100)