The year is 2046. Haruyuki Arita is a young boy who finds himself on the lowest social rungs of his school. Ashamed of his miserable life, Haruyuki can only cope by indulging in virtual games. But that all changes when Kuroyukihime, the most popular girl in school, introduces him to a mysterious program called Brain Burst and a virtual reality called the Accel World.
Taken from MAL: Accel World - MyAnimeList.net
I also agree that it's really good. All the cliffhangers in the first few eps kinda annoyed me, but that seems to have become a bit better now.