This is the game of ``Quinto'' implemented in Java by Kaolin for your enjoyment. If you're interested you can download the source code [JQuinto.java], or another implementation in Tcl/Tk [Quinto.tcl].
All squares start out black. Click a square and it and its four neighbors (above, below, left, right) will change color. The object is to turn all of the squares to white simultaneously. Useful fact: Clicking a square twice is the same as not clicking it at all, and it doesn't matter in which order you click the squares.
Next you can read a page all about the solution.