Kirito is the main protagonist, he is one of the 1000 beta testers for the first Immersive MMO, where you put on a helmet (Net Gear) which intercepts your influx and recreate them in the game. 10000 copies total were sold, and once entering the game, all players got stuck in it, unable to log out. Later on, they all get teleported to the central place of town #1 where they are announced by the game maker (akisomething) that they cant get out, nobody from the outside can help them (all explained in details but this is just a summary), and that their only way to leave the game is to beat the final boss at the 100th floor of the game. (you start at floor 1 and go higher and higher, every floor having 1 town and 1 boss). The thing is, if they ever die in the game, the Net Gear will fry their brains and they will also die in real life. And so it starts.
If you want more information or explications about certain event or of certain episodes, feel free to ask me