Centuries ago, the island of Tsushima was invaded by Mongol warriors. The Mongols slaughtered many people on the island, but a former samurai named Jin Sakai defeated them and saved Tsushima. After that, the legend of The Ghost eventually was seen as a myth, with many wondering if the Ghost was real or not.
Now in the mid-22nd century, Japan has changed quite a bit. Quirks exist now, as do superheroes and supervillains.
One young man who had no choice but to sacrifice his quirk in order to save the world, is almost completely forgotten about by the world and had to give up on his dream of being a hero.
But one day when he's on his way to work, he's approached by his father whom he hadn't seen since he was four. His father reveals to him that they are the descendants of Jin Sakai, and that it is now Izuku's duty to defend Japan as its new Ghost.