A Hero Protagonist is when The Hero and The Protagonist are the same person. This combination of roles is extremely common, to the point where it's considered true unless otherwise noted within any work. Simply put, the central character is also an established force for good within the universe. This role is used most often in classical myths and heroic legends, since these tales are usually a story of conflict between the forces of good and evil. The Hero Protagonist is also a source of Escapism; the audience sympathizes with the character because he's who they want to be, rather than who they actually are. It's common to see Hero Protagonists tackle villains who ether cause or are personifications of real-life issues, in order to fulfill the desire of the audience to see these problems dealt with.
On the other hand, these characters need to be treated carefully. Since the Hero Protagonist is the central character, the issues common in The Hero become very noticeable very quickly. Since it's inevitable that the character will win, a lot of the drama in the story is removed. Good writing will therefore focus on how they win, or offer up an interesting character dilemma. Bad writing can turn the Hero Protagonist into an Invincible Hero. Several works avoid the problem altogether by averting the Hero Protagonist, making The Protagonist less heroic and therefore more interesting, as well as shunting off The Hero, if such a character exists, into a supporting role, which allows them to be awesome and heroic without dragging down the narrative.
A Hero Protagonist is most often found in works with Black and White Morality. This is an Omnipresent Trope and easily one of The Oldest Ones in the Book, to the point where most of its aversions are likewise The Oldest Ones in the Book. For when The Hero is not The Protagonist, see Supporting Leader and Hero Antagonist. For when The Protagonist is not The Hero, see Anti-Hero, Villain Protagonist and Supporting Protagonist. Not to be confused with Hiroaki "Hiro" Protagonist.
As this is an Omnipresent Trope, no examples please.