The hero in Shakespeare's historical plays can be any character that Shakespeare choses to lift up in his writing. It might be a king, or a king's son or a citizen. (While you refer specifically to the historical plays, please note that Shakespeare's tragedies also include "the history plays with tragic designs, such as Richard II.")
Many of Shakespeare's heroes were tragic heroes. These are great ("accomplished") man, who ultimately die, and their deaths are their own fault caused by their tragic flaw. In Hamlet, for instance, Hamlet is the son of the murdered king. He is the tragic hero of the story, who dies (with everyone else); his tragic flaw is indecision.
In one of Shakespeare's historical plays, Brutus truly loves Julius Caesar, in the play by the same name. However, he becomes our tragic hero. It is not Mark Antony who seems to love Caesar as well, but uses Caesar's death to promote his own future as one of the Triumvirate (leaders) of the Roman Empire. Brutus is a Roman nobleman. Some say that his flaw is his "philosophical commitment to principle," while others argue that it could be "self-deception" in making himself believe that what he is doing (his part in Caesar's assassination) is noble and acceptable.
On the other hand, not all of Shakespeare's heroes die. In Henry V, Henry is one of Shakespeare's heroes who not only lives, but is triumphant at the play's end in defeating the French in a decisive battle during The Hundred Years War. Henry is wise, and a valiant king and warrior. He encourages his men to fight when the odds seem impossible in the favor the the French. Henry's men respect him and respond to his battle cry; meanwhile, Henry enters the battlefield as his men do—they fight side-by-side, while other kings would have been waiting, somewhere safe, until the fighting was over. Henry V was a true hero, refusing to ask of his men what he could not give himself: his life, if necessary.
There are different kinds of heroes in the historical plays. Sometimes they are tragic heroes who give their lives for a greater cause, or lose their lives because of a tragic flaw, while in other of Shakespeare's historical plays, the hero is still a great man, but he overcomes obstacles and comes out triumphant at the play's end.