Many mixers and auxillary equipment will output a large DC offset when being switched on and off, this offset can often be heard as a thump sound and can cause damage to monitors in the room if they are powered up at the time. For this reason it is recommended that the monitors be the last thing to be switched on and the first thing to be switched off in the room.
For turning things on you can think of it like a signal flow, exteral devices first, then the mixer, then the last thing is the monitors. For turning off just reverse the process; monitors, mixer, external devices. This way you will ensure no harm is done to the monitors.
If you have one breaker/switch for the complete power in the room, it is still recommended to turn the monitors on after the main breaker has been switched on and turn the monitors off before switching off the main breaker.