Beowulf is an epic that came out of a warrior culture and was used not solely to entertain but also to teach the values of this culture. The Anglo-Saxons valued bravery, heroism, strength, loyalty, fame through glorious deeds, and the desire to fight evil. Their leaders were their best warriors. Beowulf himself embodies all of these qualities, and you can find examples of these throughout the text. He is the strongest and best warrior in his country, and after he defeats Grendel and his mother (among other victories) he becomes king. Wiglaf, who becomes Beowulf's successor, also embodies these traits. When all of the other soldiers abandon Beowulf in his fatal battle against the dragon, Wiglaf does not. He displays courage and loyalty in helping Beowulf defeat the dragon, which is why he is named the next leader. It is true that Beowulf fights these monsters to help his tribe and the Danes, but he also does so for fame and glory and hopes to be remembered for such deeds, which is why, on his deathbed, he requests that a monument be erected to remember him and how great he was. In seeing this monument, future generations will remember Beowulf and the qualities he embodied, reminding them to fight evil forces with courage and strength and to always be loyal. Anglo Saxon culture did not value humility.
Another interesting aspect to note is the idea of Christianity. By the time Beowulf became a written text and not just an oral story, Christianity had begun to spread through Britain. As such, certain Christian ideals and language are sprinkled throughout the text we read. The most significant Christian value in this text is the connection between God and good. When battles against evil are won, the characters praise God and rely on him to help. However, the idea of faith is at odds with the pagan concept of fate, which is often associated with unfavorable conditions and results in the text.
So, to simply answer your question, a moral person in Beowulf is one who bravely and courageously fights evil for the sake of his people (and others) and for fame, someone who strives to be strong and is loyal to his leaders/followers; increasingly, over time, this morality also began to include a faith in God's help to win battles against evil.
The moral lesson I'm always struck with in Beowulf is selflessness. Hrothgar has been plagued by the ravages of Grendel for a long time; when Beowulf finally hears of it, he simply gets ready to leave. He gathers some men, tells the King--to whom he owes his allegiance, his time, and his talents--he's going to go. His explanation and his motivation are simple: I can defeat this marauder and rescue Hrothgar's kingdom, so I will. That is the pinnacle of selflessness.
Beowulf has a distant connection to Hrothgar, through his father, but this is not a place or a people he owes anything to for any reason. Yet, he goes because they are in need and he knows he can help. He is rewarded at the end, it's true; however, it's just as likely he could have lost his life in the effort. (He does lose one of his men, and Beowulf himself ends up battling both Grendel and Grendel's mother--an unexpected and fierce opponent.)
When I think of Beowulf, I think of the selfless civil servants--those who serve as firemen, policemen, EMTs, and so many more--all over the world who do such brave things daily without the promise of anything but a thank-you and their normal (and certainly not grand) paycheck in return. Loving one's fellow man more than one's own self is the epitome of moral thinking and action.
There are many morals in the epic poem Beowulf to be learned and understood. These morals are explained very briefly with little detail thus not being able to be completely understood. All these morals are intertwined into lessons about good and evil in a thrilling story of a hero. Some examples of these morals are that if you fight you must fight fair in order to win. Another example would be that good always triumphs over evil. These are just a few of the morals taught in the epic poem Beowulf.
Beowulf is a very altruistic hero as all hero's are and he is therefore rewarded with the accomplishment of his missions and challenges. One of his great missions was his victory over Grendel. Grendel is a monster in human-like shape descending from Cain. He lives under an inherited curse and is denied God's presence. He is also known as the "guardian of sins." Grendel is also a heathen, the physical image of a man estranged by God. His enormous size and strength make him resemble early thoughts and descriptions of Satan. Beowulf and his men slept in the mead hall one night and everybody lay awake for they feared when Grendel may come. When Grendel came crashing through the great doors of the mead hall he grabbed one of Beowulf's men who he let be devoured by Grendel. When Grendel came to Beowulf he immediately saw who he was and before Grendel could grab him Beowulf got hold of him. Beowulf fought honestly without weapon because Grendel did not have a weapon either therefore Beowulf would be shamed if he slew Grendel with a sword. After pulverizing Grendel he finished him off by tearing off his arm which Grendel then fled and died. The great arm of Grendel was hung above the mead hall. This lesson teaches us that if you fight fair you are destined to win.
A second moral taught in this poem is that good must always triumph over evil.
One could be this: If you have a gift, you should use it not just for yourself but also for others. Beowulf was given immense strength and bravery, and he did not use it just to become famous, he did save the Danes from frightful monsters.