In a nutshell, Spider-Man represents the reverse of almost every other superhero's "secret identity" concept.
Most superheroes are defined as "they look like normal people in everyday life, but secretly they are superheros." The distinction is how their normal appearances are contrary to the reality of who they are.
For Spider-Man, though, he's defined as "he looks like a superhero in his superhero life, but secretly he's just a normal, kind of dorky guy." The distinction is how his seemingly glamorous masked appearance is contrary to the reality of who he is and what his life is really like. The reverse spin is extremely important to understanding his character and to understanding why he is so popular. This, by the way, is also an insight into one of the problems in recent decades with making Super-Man more relatable and popular with audiences: The comics and most recent film moved too far toward the "messiah alien" depiction, and people weren't able to relate to him enough anymore.
Spider-Man's biggest obstacles are not the supervillains he fights but the daily struggles in his difficult, ordinary life. He feels unpopular. He can't pay his bills. He has relationship troubles. He's perpetually worried about disappointing his Aunt May (who is his "mother," basically). He has to go to school and do homework and wash his Spidey costume, and so on. Even when he's saving the city as Spider-Man, the public insults him and the press hounds him and he's unpopular and unappreciated. His boss is a jerk who underpays him and treats him like dirt.
Spider-Man strikes a chord with people because they relate to him. He's not rich, he's not a playboy, and he gets beat up a lot even though he's a superhero. He's young, he makes a lot of mistakes, and his emotional ups and downs are a driving force in the stories.
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