Why do my lights dim when my air conditioner starts?

This is usually not a good sign. When your lights dim at the start up of the air conditioner it is a good indication of a compressor pulling too much amp draw at start up. Your Air Conditioning Technician needs to have a look at it and take a reading with his amp meter to see exactly how high the draw is and make the appropriate decision as to what should be done at that time. Sometimes simply adding a compressor hard-start kit will help lower that starting amp draw.