Izuku (Deku) Midoriya has a dream. He will go to prestigious U. A. High School where all the most famous superheroes graduated and become the next great hero to protect the world. The only catch is that Deku is quirkless. He's part of the 20% of the population that has absolutely no powers. Can't move things with his mind, can't set things on fire. Definetely, can't fly. But Deku has faith that if he works hard and studies every superhero and villian out there (ALL OF THEM. He has at least 13 notebooks full of observations) he can make it anyway. When his willingness to put himself in danger to protect others (yay?) catches the attention of the world's most powerful hero, All Might, Deku gets the chance to live his dream. But first he has to survive All Might's training the school's rigerous system.
Not as crazy and nonsensical as One-Punch Man, or as serious and dark as western superhero comics. My Hero Academia fits nicely in the middle. Unlike the typical manga hero who's either a clueless kid with immense powers, or a Sherlock Holmes type schemer, Deku is an optimistic thinker. He specializes in analyzing situations but without the cold detachment we're used to seeing. It makes for a refreshing twist on both stereotypes. There are also plenty of twists and turns to the plot that I don't want to spoil. Basically, this manga plays up all the tropes you'd expect from a battle manga about people with super powers and then twists it just enough so you never quite know what to expect. Light-hearted manga, with a bit of a punch.