In Mahjong Solitaire you take Mahjong tiles and match them in order to clear the board. Keep in mind there are some special tiles that'll match together which can be denoted by the colorful background that is different than the usual white tile backgrounds.
Note that that each pair of tiles appears twice, and so is on the board 4 times. This is important to know in order to maximize your chances of victory. As sometimes you will need to remove the pairs in a particular order in order to win.