Why are the lights flickering when the a/c is on?
Im going to assume you are talking about either a window air conditioner or portable unit - not central AC.

The lights flickering means the voltage is dropping.  Incandescent bulbs are particularly sensitive to that.  Most CFL and LED bulbs flicker less, though some may still flicker.

The voltage is dropping because of a large current draw.  It is normal for there to be a momentary large draw as the compressor starts up.  Fridges and freezers do the same thing.  Its part of the reason for having a dedicated circuit for such appliances.  The manual for your AC may even say it requires a dedicated circuit.

If its doing this when the AC first turns on, its not a problem.  If it were drawing too much power for too long your circuit breaker would trip.  If the compressor is starting and stopping rapidly causing constant flicker, your AC unit needs servicing or replacing.  The noise might be the compressor or a fan dying, or just vibrations.  Hard to tell without hearing it.