Atomic chess is a variant where you *destroy* the pieces: the pieces explode. According to Wikipedia, "Standard rules of chess apply, but all captures result in an 'explosion' through which all surrounding white and black pieces other than pawns are removed from play."
Quoting claymore, Atomic chess' rules are: "pieces explode when capturing, destroying the capturing piece, the piece being captured, and all pieces (but not pawns) in a one-square radius."http://en.lichess.org/forum/lichess-feedback/atomic-chess#1
for more info. Here are the rules that lichess is going by http://www.freechess.org/Help/HelpFiles/atomic.html
according to this post http://en.lichess.org/forum/lichess-feedback/atomic-chess-beta#1
You can play games with the atomic chess variant: click the "create a game" button (or the "play with a friend button" - you can't play this variant versus the machine yet) select "Atomic" as the variant.
Hope this helps! :)