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Old Hamlet killed Fortinbras in battle, and young Fortinbras (Prince of Norway) is determined to avange his father and win back his lands.
Fortinbras is the son of the former king of Norway. His father fought with Hamlet SR, mano-a-mano; the winner got all of the land from the losing kingdom. Hamlet SR beat the king of Norway, so Denmark inherited all of Norway's land. Fortinbras JR (in this play) wants the land back so he wants to march against Denmark. The Norwegian king, old and infirm, does not want that to happen, so he will tell Fortinbras JR not to march.