In chess, tresesponded to. In this case, since both players have "lost" a tempo, the net result in terms of time is nil, but the change brought about in the position may favor one player more than the other.
Gaining tempo may be achieved, for example, by developing a piece while delivering check, though here too, if the check can be countered by the development of a piece, the net result may be nil. If the check can be blocked by a useful pawn move which also drives the checking piece away, the check may even lose a tempo.
In general, making moves with gain of tempo is desirable. A player is said to have the initiative if they are able to keep making moves which force their opponent to respond in a particular way or limit their responses. The player with the initiative has greater choice of moves and can to some extent control the direction the game takes, though this advantage is only relative, and may not be worth very much (having a slight initiative when a rook down, for example, may be worthless).
In some endgame situations, a player must actually lose a tempo to make progress. For example, when the two kings stand in opposition (a form of zugzwang), the player to move is often at a disadvantage because he must move. The player to move may be able to triangulate in order to lose a tempo and return to the same position but with the opponent to move (and put him in zugzwang). Kings, queens, bishops, and rooks can lose a tempo; a knight cannot (Muller & Pajaken 2008:40,175,189).
In the position from a 2008 game between Artyom Timofeev and Ernesto Inarkiev, Black resigned because White will win with a tempo move. (Timofeev won the 2008 Moscow Open with this game.) White is threatening 118.Rh8+. If Black moves his king on move 117, White wins the bishop with 118.Rh8+, which results in a position which has an elementary checkmate. If Black moves 117...Bh5 then 118.Rh8 and Black is in zugzwang, and loses. So Black must move 117...Be2 to avoid immediately getting into a lost position. But then will come 118.Rh8+ Bh5 and now White makes a tempo move with 119.Rh7 (or 119.Rh6), maintaining the pin on the bishop, making it Black's turn to move, and Black must lose the bishop.