In the tale (epic poem) of Beowulf, the evil that Grendel and his mother represent seems to be that of original sin. While the author tells the story of Grendel and later his mother, along with the history and brave exploits of this hero (a Geat) from a foreign land that has come to help the Danes in their time of dire need, the reader also learns of the origins of this evil.
It should be noted that the original version probably did not include references to religion, believed by many to have been a pagan story originally. However, the story was shared in the oral tradition (by word of mouth) for many, many years before being written down. During that time, the scops (storytellers) were introduced to the theology of Christianity, and Christian elements became a part of the weave of the story we have today.
So new was Christianity that the Biblical references in the poem relate only to the Old Testament...
One of the most important elements in Christianity is original sin: the temptation of Adam and Eve by evil personified as a serpent, when they turned their backs on God's law about the Tree of the Knowledge of Good and Evil. Knowing what they have done, God banishes them from the Garden. The next important part of the story involves the couple's sons: Cain and Abel. Abel makes a sacrifice to God that is pleasing to Him; Cain's sacrifice is half-hearted and does not please God. In a fit of violent jealousy, Cain murders his brother: the first murder in God's creation. Based on this information, it is important to recall that according to the storytellers, Cain was cursed, as were his offspring. Note the segment from Chapter One:
Thus the clan’s life was one of good cheer and revel until that fiend of hell began to work evils. Grendel was this grim beast called, who haunted the moors and secluded fens; this accursed one had long dwelled with monsters since the Creator had decreed his exile. On the kin of Cain did the sovereign God avenge the slaughter of Abel; Cain gained nothing from this feud and was driven far from the sight of men for that slaughter. From him awoke all those dire breeds: ogres, elves, and phantoms that warred with God a lengthy while; He paid their wage to them!
In this background provided at the story's beginning, we realize that Grendel is descended from the cursed Cain, and included in the monstrous types listed (ogres, elves, etc.). The sounds of joy and celebration coming from the mead (drinking) hall elicit such rage in the beast, that he breaks in, grabs the first victim he can lay his hands on, and devours him whole. Sometimes he takes another with him. His evil continues for twelve winters until Beowulf, having heard of Hrothgar's suffering and the devastation the monster visits upon any in the mead hall, comes to deliver them from the scourge of Grendel. (It is after his destruction that Grendel's mother comes, seeking revenge.) Based upon the introduction, Grendel and his dam (mother) are representative of original sin, specifically the evil of the first murder.