The illustrated, animated schematic shown below displays three motor starters each with start stop buttons.
The starters are interlocked so that MS1 must be running before MS2 can start and MS2 must be running before MS3 will start.
Interlocking starters are sometimes necessary when a certain motor must be running before others may be started. If the first motor should fail from overload it will shut down all other interlocked to it.
e.g. If a grain elevator moves grain up to a screw conveyor and the screw conveyor transports it to a silo, the screw conveyor must be running before the elevator otherwise the grain from the elevator will have no place to go, possibly jamming up the elevator or overflowing the grain. If the screw conveyor fails from overload the interlock will stop the elevator.
The animated schematic will show how this is done, normally open auxiliary contacts are used to control the path of the circuit, they work just like a stop button.
When the starter is on the auxiliary contacts close and the path is available for the start button to complete the path to the coil of the next starter.