This is a fantastic question. When we look at the great epics of the Western world, a number of characteristics emerge.
First, epics center around a single hero. For example, the Iliad is about Achilles and his wrath; The Odyssey is about Odysseus and his homecoming; the Aeneid is about Aeneas and his journey to find a new land. Beowulf is about the hero Beowulf. More specifically, it is about Beowulf’s conflict with Grendel and the dragon.
Second, often epics come from oral tradition. Beowulf shares this in common with the Iliad and Odyssey, which come from oral tradition as canonized by Homer. Also epics are in poetry. This might seem odd, but the poems of Homer and Vergil are written in dactylic hexameter and Beowulf in alliterative verse or alliterative poetry.
Third, epics have a big one-on-one contest. Achilles fights Hector, Aeneas fights Turnus, and Beowulf fights Grendel and the dragon. Moreover, these duels are for honor and glory. It is important to note that when Achilles is given the decision not to go to Troy and live an old life or to go to Troy but die a death of glory, he chooses the latter. Likewise, Beowulf fights for glory and honor. This says something about the culture in which epics thrive.
Fourth, epics have a theistic worldview. In the Greek and Roman epics, the gods are ubiquitous, fighting for and against the characters. In Beowulf we are dealing with a different historical context, but there is a divine element – the Christian God is present.
Fifth, epics have formulaic sayings – probably a relic from oral tradition. For example, Weox under wolcum is a formula is Beowulf, which is repeated in lines 651, 714, 1119, 1374, 1631, and 1770.
Finally, epics usually have a journey. The Greeks travel to attack the Trojans; Odysseus travels back home to fight the suitors; Aeneas journeys to Italy; Beowulf travels to the land of the Danes.
These points should get you started.