The answer can be found in the rules of combat during the Elizabethan age. King Hamlet and King Fortinbras led their armies of Demark and Norway, respectfully, into battle. As the rules of combat (and an old adage) say, to the victory goes the spoils. In this battle, King Hamlet defeated King Fortinbras and, in so doing, gained all his land and titles.
It is after this fact that it get tricky. Common sense, and the laws of hierarchy, would say that the kin of the former king should rightfully gain the throne. However, in the case of Fortinbras (and Hamlet) the title of king instead went to other members of the family. In Hamlet's case, it went to his mother (not surprising since Queen Elizabeth, the reigning power of England, gain power almost the same way), who surprisingly married her brother-in-law Claudius (King Hamlet and Claudius were brothers). The same thing happened to Fortinbras, whose rightful throne went to his uncle, who happens to be named Norway (confusing, i know). So, both Hamlet and Fortinbras are left with not but title. So Fortinbras decides to build an army in the outskirts of Norway and forcefully seize his land back from Denmark.
So, to re-cap:
- Hamlet Sr. and Fortinbras Sr. fight; Fortinbras loses; rules of combat says that Hamlet Sr. gains all the land of his oppenent.
- Fortinbras Jr. should be king (so should Hamlet Jr.); confusion reigns when uncles take throne (in both cases)
- Fortinbras Jr. now wants to take the land back by force.
What I can find in the eNotes is that he lost them in battle against King Hamlet-- the same battle which claimed his life. I believe young Fortinbras is angry because, like Hamlet, he lost his rightful throne after his uncle took power.
this is stated by horation in response to questions from the watchmen in I.I.
horatio, however, sounds SOOOOO much like a lawyer it can be hard to make out.
also, i was under the impression that some european countries in antiquity passed the crown down between brothers before giving it to the eldest born male. so i am not entirely sure that fortinbras and hamlet have been passed over. claudius himself says (to hamlet) that the prince is next in line for the crown.
regardless, old hamlet beat old fortinbras in a one-on-one fight (as opposed to claudius's conniving murder and fortinbras' (and claudius's) creation of an army. this shows the nobility, honor, and self confidence of the old king; foiling it against the actions of the other two "leaders" in the play.