Note that one one of the contactor acts as a switch for the start button.
Start stop circuit contactor.
The most common use of 3 wire control is a start stop control.
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.
Basiclly you press start button which powers the coil which then pulls in the contactor once the contactor makes the feed from the stop button holds the coil in untill the stop button is pressed which breaks the circuit.
The contactor is operated by the control circuit energizing a coil as in the example above.
See image below for an example of 3 wire control being used to pull in a contactor to start a 3 phase motor.
A simple circuit diagram either of the two start buttons will close the contactor either of the stop buttons will open the contactor.