Laertes is the son of Polonius as well as brother to Ophelia.
During the course of the play, we find Laertes as a scholar and devoutly loyal to his family.
When Hamlet murders Polonius, Laertes becomes blinded with rage and fury that he wants to murder Hamlet. King Claudius builds on that hatred of Hamlet and encourages Laertes to rid Hamlet once and for all. Hamlet, immensenly sad because he had killed Polonius and agrees to fight a duel with Laertes.
Before the fight, Hamlet apologizes to Laertes. Laertes accepts it, but feels he must still fight for honour. Following a comment by Hamlet which he takes as an insult, he attacks and they both end up getting cut by the poisened sword.
As he lies dying, he tells Hamlet that Polonius is the bad guy. With his last breath, Laertes exchanges forgiveness with Hamlet.