Miles Morales, aka Spider-Man
The movie manages to stick pretty close to its main character's on-page origins, some needlessly complicated universe-merging from the comics notwithstanding. In 2000, Marvel launched its Ultimate Comics line, which re-imagined classic characters in a more contemporary setting and with a more serious tone. The first and most successful title in the line was writer Brian Michael Bendis and artist Mark Bagley's Ultimate Spider-Man, which introduced a new Peter Parker and re-imagined many of the Marvel Universe's villains and heroes. As the series progressed, it became apparent that this new Peter Parker wasn't following the previous one's life exactly (even if he did also have to endure a "Clone Saga") -- and, in 2011, he died defending Aunt May from the Green Goblin. In the Ultimate Universe, Peter Parker is remembered as a hero and everyone feels a little guilty that they, as a community, let the teenager perish.
Which is where Miles Morales, a black Puerto Rican resident of Brooklyn, steps in. His uncle, Aaron Davis, who also happens to be the low-level Marvel villain the Prowler, steals some stuff from an Oscorp lab, including a spider engineered to endow the powers of Spider-Man. The spider later bites Aaron's 13-year old nephew Miles, giving him similar powers, such as increased strength and the ability to stick to walls, but also two powers unique to the character: a "camouflage" mode that can render him and his clothing invisible to the naked eye, and a "venom strike" which is some sort of delayed energy "sting" that looks very, very painful.
After Peter Parker's death, Miles toys with the idea of becoming the new Spider-Man, but gets discouraged when his uncle figures out his big secret and wants to use his nephew's new powers to increase the profile of the Prowler's hauls. Miles confronts his uncle, and his venom blast accidentally shorts out the Prowler's equipment, causing an explosion that kills him. Now, Miles can't tell his parents about his power or his true identity, and he's attracted the attention of the Ultimate Marvel Universe, as well. Aunt May and Mary Jane track him down and gift him Peter Parker's webshooters. Nick Fury and S.H.I.E.L.D. initially try to discourage Miles, but end up making a costume for him when Nick determines the kid has a good heart.
A lot of horrible stuff befalls Miles in the Ultimate Universe (e.g., his dad essentially disowns him after his mom is killed by Venom), until a 2015 publishing event called Secret Wars smashed Miles into the main Marvel universe with an adult Peter Parker. In the new storyline, his parents are both alive and he has a good relationship with them, because why be so hard on the littlest Spider-Man? Currently, Miles Morales is the Spider-Man who's most focused on New York City -- when he's not leading the teenage superhero team the Champions, that is.