"Sword Art Online," or shortly SAO, is a light novel written by a Japanese author, Reki Kawahara, and with illustrations by ABEC. The story revolves around various virtual reality MMORPGs played, among others, by Kazuto "Kirito" Kirigaya and Asuna Yuuki.
"Fairy Dance" is a sequel to the events taking place in SAO, where the players have been somehow transported into the game they were playing. In Fairy Dance, we learn that there were 6,147 surviving players and that they were able to log out successfully.
This is true for Kirito as well, but not for Asuna, whom the former fell in love with. If you read SAO, you need to read this arc as well, to see if Kirito is willing to go back into the virtual world and try to save Asuna, and find out if there's a happy ending or not!