The above answer gives a great explanation of how the Christian scribe who wrote down Beowulfas it exists today would have seen these characters—or wanted his readers to see the characters—within the poem. As that educator has also noted, however, Beowulf did not begin life as a Christian text....
The above answer gives a great explanation of how the Christian scribe who wrote down Beowulf as it exists today would have seen these characters—or wanted his readers to see the characters—within the poem. As that educator has also noted, however, Beowulf did not begin life as a Christian text. The Christian elements in Beowulf are later interpolations, and in many ways they sit oddly alongside the pagan context in which Beowulf and his warriors actually live.
The Germanic society depicted in Beowulf is set in a pre-Christian time, and this is observable in the way that Beowulf, Hrothgar and the others enact kingship and social customs. Within the context of this society, then, Grendel represents the outsider, or the "other." He's connected to Cain in the final version of the poem, but this is largely just because the Christian reader would understand what Cain symbolized—someone who had strayed away from "good" society and become something other than what was acceptable.
The Anglo-Saxons had an enormous fear of being exiled from the group. This is expressed in many of the elegies, such as The Seafarer and The Wanderer. Grendel, too, loathes being exiled; the poem suggests that it is the pain of exile that has, in many ways, warped him. Because he is envious of the inhabitants of Heorot, he begins to attack them. He wants what they have. He is the exile, the person who has not obeyed the rules of society and who now attacks it from the outside. In many ways, we can argue that Grendel represents the very danger of failing to adhere to social customs in and of itself: if you do not do what is expected of you, within a culture which requires lords to provide for their vassals and vassals to die for their lords, the whole structure of that society collapses.
Grendel's mother is an extension of this symbol—but she's much more complicated. Anglo-Saxon scholars have noted that the word aglaec is attributed to both Grendel's mother and Beowulf. In Grendel's mother's case, it has traditionally been translated as "monster," whereas when describing Beowulf, it becomes "hero." Some have argued that Grendel's mother is actually not a monster within the original context of the poem, as she is avenging her son's death and therefore performing the appropriate heroic function expected of a surviving kinsman. Another term, idis, applied to Grendel's mother, is often translated as "lady" but has connections to Norse terms describing the Valkyries and again suggests that to interpret Grendel's mother as a monster is to fail to understand the poem's pre-Christian context. Rather, she may represent the restoration of balance within the pagan world. Yes, Beowulf has to kill her, but in launching an attack in retaliation for her son's death, Grendel's mother has actually behaved, as it were, correctly.
The dragon in Beowulf, meanwhile, is more straightforward. Again, it represents evil, but of a different kind. As a king, Beowulf has to defend his people against all external threats. The dragon is a representation of these many threats and challenges which might face a good king and a noble people.