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, and the terms are often (falsely) assumed to be synonymous and used interchangeably. Simply put, the central character is also an established force for good within the universe. 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 these tackle villains who either 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 (usually), 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 by having the two traits in different characters, or dropping one or both from the narrative completely. If The Hero is made into a supporting role, this 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, where they will be opposed to the Villain Antagonist. This trope is 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, Hero of Another Story 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.