What is a superhero?
It does not seem unreasonable to define the term. Granted, a certain sort of person dismisses such attempts as bound to fail given that exceptions will always exist to any definition--but the existence of ambiguities does not, as such, keep definition from being a useful, in fact essential, tool for making sense of reality. (The map may not be the territory, but that does not make maps useless, no matter how much contrarians addicted to stupid epistemological nihilism natter on.)
A good starting point for such a definition is an examination of those criteria that may seem least dispensable to the conception of the superhero as we know them today--the superhero tradition as established in the comic book medium, especially from the advent of Superman forward.
1. They Must Be Both a Hero--and Super.
A superhero must obviously be a hero--a figure that does something both positive and extraordinary such as is worthy of admiration by others. Where the superhero's sort of heroism is concerned there is an expectation of service to the community of some physical kind, usually entailing courage in the face of physical danger, to save the lives of others because it is the right thing to do rather than a matter of self-interest; with such action a
vocation rather than an exceptional incident. Of course, people pursue vocations that have them performing such acts--firefighters are the go-to example--but superheroes are distinguished from them in that they are
super, their abilities exceeding the human norm in a way which is quantitative or qualitative or both. (Conventionally the firefighter running into a burning building must make do with "merely" human physical and mental capacities, but a superhero might be able to put out the fire with a blast of icy breath, as Superman can.)
2. They Have a Very Distinct and Very Public Persona, of which Distinct Powers, Codenames and Physical Appearances (Usually but Not Always a Function of Costuming) Tend to be a Part.
The above seems to me mostly self-explanatory. In contrast with, for example, heroes who are secret agents, who are likely to conceal their "heroic" aspect behind cover identities as they set about their work, the superhero's cover identity, their public persona, is itself heroic--and indeed advertised to the world at large, the more in as its elements include the aforementioned matters of a power, or powers, that tend to be very individualized; a similarly unique codename; and a unique appearance, usually but not always derived from a costume. (Barry Allen is a hero made a superhero by his possession of "speedster" capabilities such as even other DC superheroes tend not to have to fighting evil; is, appropriately, known as the Flash, after his speed; and wears a red costume with lightning bolt insignia, also evoking that speed. Other figures such as Marvel's The Hulk and the Thing have distinct powers and codenames, and their distinct appearance--albeit less reliant on any costume in their case.)
3. The Superhero's Activity is Highly Individualistic.
As implied by the exceptional character of the hero's capacity, and their conspicuous public persona, the conception of the superhero is individualistic in
action. Consider, for example, the firefighter and secret agent both. Both figures are conventionally employees of a public agency, which pays them money to do a job in line with orders--which does not make a sense of duty irrelevant by any means, but still raises the question of the paycheck, career, etc. in ways that unavoidably give their activity a different texture. Both also rely on their organizations for their ability to do their jobs--unlikely to have equipment or other supports necessary to their hero task if they were not so employed. By contrast the superhero is ordinarily alone, answering to no one--taking no orders, and often having a complex and fraught relationship with authority (epitomized by stories in which Batman falls afoul of the law), all as what equipment they need is their own (one reason why superheroes are so often independently wealthy, as Batman or Iron Man is).
Moreover, when we see superheroes "team up," teaming up is exactly what they do--these individuals cooperating in a joint effort rather than relinquishing their identities to be
good "organization" men and women. (Iron Man is first and foremost Iron Man, and never "just" an Avenger.)
Of course, much else tends to go with this. The public persona is often a way of concealing a private identity, and at least attempting to protect a private life. And of course there is apt to be the unusual origin story--for superhuman abilities, and the decision to put on a costume and fight a private war against crime or some other such evil are the kinds of things for which most people expect an explanation, which is likely to be extraordinary because of what has to be explained. (Thus is Superman literally from another planet, while Batman has been motivated by childhood trauma and equipped by a lifetime of preparation for his vigilante mission, aided by vast wealth as well as extraordinary talent.) One may add that the superhero almost always faces a super
villain at some point--because any other sort of villain is a less than worthy adversary. (How long would Superman remain interesting just catching small-timers like purse-snatchers?) However, those three items seem to me to constitute the indispensable minimum--with any character not meeting those three criteria, which I think enable us to distinguish between superheroes and non-superheroes of various kinds, without bounding the category so narrowly as to deprive it of analytical usefulness, and permitting distillation as the following:
A superhero is a figure who, acting on their individual initiative and resources, and through a distinct public persona apt to entail codename and (usually costume-based) appearance, makes a vocation of defending the public from physical dangers such as accident, crime and "supervillainy," usually in a way requiring physical action and courage on their part, and drawing on abilities and/or equipment endowing them with more than ordinary human physical and/or mental capacities.