The objective of the game is to change all zeros to ones. Clicking on any of the buttons changes the button and its immediate neighbors (above, below and besides). When the option "cylinder" is selected it behaves like a cylinder (i.e. top and bottom of rectangle are glued) and likewise for the option "torus" or "moebius". Press "reset" to start or to play again. You can change the dimensions to any numbers up to twenty.
The game is based on the game Fiver from Mazeworks.com. There are also versions called Merlin's Magic Squares and Lights Out which are sold as handheld puzzles. Here is a page on Lights Out. The paper "The sigma game and cellular automata" (American Math. Monthly, 97 (1990) 24-34) by K. Sutner has the game's theory and a bunch of references.