Definition: A computer or console game where you normally take control of armies of animated figures or characters, direct their development, and fight their battles. The reference to Real Time is mainly due to the fact that the game continues to run even if you are not actively giving commands, although during solo games the game play can usually be paused. Such is not the case in multiplayer games for obvious reasons.
Examples:
Rise of Nations for the PC is a RTS game that has won several awards from the gaming community.