In chess, tempo is a "turn" or single move. When a player achieves a desired result in one fewer move, the player "gains a tempo"; and conversely when a player takes one more move than necessary, the player "loses a tempo". Similarly, when a player forces their opponent to make moves not according to their initial plan, one "gains tempo" because the opponent wastes moves. A move that gains a tempo is often called a move "with tempo".
A simple example of losing a tempo may be moving a rook from the h1-square to h5 and from there to h8 in the first diagram; simply moving from h1 to h8 would have achieved the same result with a tempo to spare. Such maneuvers do not always lose a tempo however—the rook on h5 may make some threat which needs to be responded 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 in material, for example, may be worthless).
In the Scandinavian Defense, after 1.e4 d5 2.exd5 Qxd5, if White plays 3.Nc3 the knight attacks Black's queen, forcing it to move again, and White gains a tempo. A similar move gains a tempo in the Center Game opening.
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 (Müller & Pajeken 2008:40,175,189).