Why are the Danes preparing for war?

Horatio explains that the Danish army is preparing for a possible invasion by Fortinbras, Prince of Norway. We learn that Fortinbras’ father (also named Fortinbras), was killed many years before in single combat with Old Hamlet, the now-deceased king whose ghost we have just seen. Now that Old Hamlet has died, presumably weakening the Danes, there is a rumor that Fortinbras plans to invade Denmark and claim that lands that were forfeit after his father’s death.