It's difficult to summarize the entire franchise (through season 2) in a single sentence, so I'll split it up by arcs, ignoring the small arcs. These may have slight spoilers, but I try to keep it limited to the introduction elements of each arc. It's not as short as Dimitri's, but it helped when I was convincing my friends to watch. ¯\_(ツ)_/¯
Season 1, Arc 1:
A technology has been developed that allows users to fully insert themselves into a video game to the point where they cannot sense the outside world at all. During the first release and testing of this technology, the developer changes the program so that the players are trapped and the game becomes their life. In order to leave, they must beat the game but with one deadly twist: if they die in the game, they die in real life.
Season 1, Arc 2:
At the end of season 1, the game is completed and most players are released, but some of the players have still not woken up from their game-induced coma. The main character from the first arc (Kirito) notices that Asuna (another teammate from the game) is one of those who hasn't woken. More games are created using the same immersion technology, and eventually a picture circulates for one of the more popular ones. In this picture, there appears to be a girl trapped in a cage. Kirito believes that girl to be Asuna and joins the game to save her.
Season 2, Arc 1:
Another immersion game goes wrong. A player appears to have the ability to kill players in the game and to have them die in real life. Kirito, with his vast experience with these games, is asked to join the game to do reconnaissance and to try and stop the killer.
Season 2, Arc 2:
I really need to rewatch this one, and it's my favorite, so I don't want to spoil anything.