The plot of Beowulf is the heroic quest. In Beowulf's case, that quest is to claim his place in eternity. In Norse mythology, however, to gain admittance to "heaven" (Valhalla), the warrior must die in battle. Hrothgar should be the one to protect his own kingdom, but Beowulf, the outsider, has to do it for him. The fact that Beowulf fights the monster alone and unarmed makes his victory that much greater. You can think of Beowulf as the Viking equivalent of the Greek Heracles or the Roman Hercules.
The main plot of Beowulf concerns Beowulf's heroic defeat of the monster Grendel and later his mother. The story opens as the great mead-hall of the Danes is being visited nightly by Grendel, the monster who devours anyone he finds. No one in the Danish kingdom is strong enough to fight Grendel, but the great Geatish warrior Beowulf comes to the rescue and kills the monster with his bare hands the first night he is there. Then Grendel's mother comes to obtain revenge for the death of her son, and mighty Beowulf kills her even though he has to swim to the bottom of a lake to do so.
Beowulf later returns home to the Geats and becomes king. The book follows his future exploits until his death in a battle with a dragon.