This is how the game timer works:

In some games (like Chess), you start out with an initial time on your clock, say three minutes, and an increment time of one minute. When it's your turn, your clock ticks down until you make a move. When you finish your turn, the increment time is added to your clock if you took less than a minute, and is subtracted from your clock if you take longer than a minute. If your clock ever gets to zero, you lose.

In other games (like Pool), the timer works a little differently. If your time expires, the turn is passed to your opponent, but the game continues.