Chess clocks, often called game clocks – like the 1970s Seiko QZ 568B chess clock here – were first used extensively in tournament chess, with the purpose of keeping track of the total time each player takes for their own moves to ensure neither player overly delays the game.
 
Consisting of two adjacent clocks with buttons atop the device to stop one clock while starting the other, the two clocks never run simultaneously.  Chess clocks are used in chess and other two-player games where the players move in turn (and in some legal settings, wherein each side is allotted a specific amount of time for arguments).  The overarching purpose is to keep track of the total time each player takes for their own moves.
 
Analog clocks – like the two red ones on the QZ 568T here – are equipped with a "flag" that falls to indicate the exact moment the player's time has expired.  Analog clocks use mechanical buttons and depressing the button on one player's side physically stops the movement of that player's clock and releases the hold on the opponents.
 
The players may take more or less time over any individual move. The opening moves in chess are often played quickly due to their familiarity, which leaves the players more time to consider more complex and unfamiliar positions later.  In fact, it isn’t unusual in slow chess games for a player to leave the table, but the clock of the absent player continues to run if it is their turn, or starts to run if their opponent makes a move.
 
The simplest time control is "sudden death", in which players must make a predetermined number of moves in a certain amount of time or forfeit the game immediately. A particularly popular variant is blitz or rapidplay chess, wherein each player is given a short time, for instance five minutes, on the clock in which to play the entire game.
 
Game clocks of this design were used in a chess tournaments beginning with its debut during an 1883 tournament held in London.  Invented by Thomas Wilson of the Manchester Chess Club, the clock has been in use since, and spread widely to most every two-player tournament game, to include like Scrabble, Shogi, Igo, Go, etc. 
 
In a tournament, the arbiter typically places all clocks in the same orientation, so that they can easily assess games that need attention at later stages.