The classic eight by eight board game, also known as Reversi. Every disc is black on one side and white on the other. On your turn you place a disc on an empty square so that an unbroken line of your opponent's discs lies between it and another disc of your own. That whole line flips to your color, and several lines can flip at once, diagonals included.
You may only play a square that flips something. If no such square exists, the turn passes back to your opponent. The game ends when the board is full or neither player can move, and whoever has more discs of their color wins.
Good play takes patience. The corners are the most valuable squares, because a disc in a corner can never be flipped again. So avoid playing next to an empty corner, especially diagonally, since that hands the corner to your opponent. In the opening and the middle game, don't grab discs: it is better to flip few and leave your opponent as few moves as possible. The disc count only matters at the end.