Reversi is an ancient game of strategy. Today most people know it as Othello. Because of all the automated piece flipping, Reversi is especially suited for on-line play.
On each move, you add one of your pieces to the board in such a way as to outlflank a row of your opponent's pieces (i.e. a row of your opponent's pieces ends up with one of your pieces on each end). Upon outflanking a line of opposing pieces, those pieces are flipped over and become yours.
The complete rules to the game of Reversi (Othello) are contained in a text file in Outland's Documentation folder.