The most common use of 3 wire control is a Start/Stop control. See image below for an example of 3 wire control being used to pull in a contactor to start a 3 phase motor. When you press the start button and the stop button is not pressed, the 24VDC relay energizes and it pulls in the R1 contactor that feeds three phase power to the motor. It also pulls in a contact that is tied in parallel with the start button giving it another path for current flow once your release the start button. This "latches" the relay until the stop button is pressed.
Here is an animated example of how a start stop circuit works.