It's called Go — originally an ancient Chinese strategy game.
The two players alternately place black and white playing pieces, called "stones", on the vacant intersections of the grid. The object of the game is to use one's stones to surround a larger total area of the board than the opponent. Once placed on the board, stones may not be moved, but stones are removed from the board if captured; this is done by surrounding an opposing stone or group of stones by occupying all orthogonally-adjacent points. Players continue in this fashion until neither player wishes to make another move; the game has no set ending conditions. When a game concludes, the controlled points are counted along with captured stones to determine who has more points. Games may also be won by resignation.