Fortinbras is a Norwegian prince who seeks revenge for his father's death. (Old Fortinbras, former King of Norway, made a bet with Old Hamlet and wound up losing his life and some important Norwegian territory in the process.) In the play, young Fortinbras attempts to reclaim the land his father lost.
Sounds like a familiar scenario, right? Fortinbras is an important foil for Prince Hamlet, who has also lost a father and now finds himself seeking revenge. But, while Hamlet sits around contemplating life and death, Fortinbras takes clear and immediate action by raising an army to reclaim Norway's lost territories. Though his uncle (the current king of Norway) diverts Fortinbras from attacking Denmark, in the end, prince Fortinbras helps himself to the Danish throne. (Remember, he conveniently arrives at the court in Elsinore immediately after the bloodbath in Act V, Scene ii.)
Lurking behind the stories of both Fortinbras and Hamlet is the question of why their uncles are wearing the crowns that should, in the normal pattern of who-gets-to-be-king, go to them (the sons). Fortinbras seems to be dealing with his impatience by going out and conquering other countries.
Hamlet, in contrast, only mentions the fact that Claudius has "popped in between the'election and [his] hopes" (in other words, his hopes of becoming the King of Denmark). Hamlet distracts himself with thinking, not with conquering. Our prince compares himself explicitly to Fortinbras when he passes Fortinbras's armies in the fields and he sees Fortinbras as a model for how he should behave. "To be great / is not to stir without great argument / but greatly to find quarrel in a straw / when honor's at the stake" (4.4.52-55). In other words, Hamlet realizes that Fortinbras doesn't have very good reasons for leading an army against Poland – but he concludes that reasons are unimportant. To be a great man is to act for any reason to preserve honor. Fortinbras, like Laertes, is an example of action with little thought – precisely the opposite of Hamlet.