Mortimer is an English nobleman. At the beginning of the play we learn he's been captured by the Welsh Glendower and his troops have been slaughtered. King Henry refuses to ransom him from his captors and accuses Mortimer of being a traitor. We also learn that Mortimer was named heir to the throne by King Richard II, which is probably why Henry doesn't want him around. [Note: Technically, Edmund Mortimer (the character in the play) is not the same historical Mortimer that was next in line to be king.] The Percy family uses the Mortimer situation to justify their rebellion against King Henry, making Mortimer an important figure in the play.
Literary critics note that, because Mortimer has married Glendower's daughter and joined the Welsh rebels, in the eyes of the English, he's "gone native." He also never actually makes it to the battle at Shrewsbury, which may be an indication that his sensual relationship with his wife may have caused him to go soft. In many ways, Mortimer's loving relationship with his wife is a foil to Hotspur's relationship with Kate because Hotspur rejects a physical relationship with his wife in favor of warfare.