It is normal for your car’s AC compressor to cycle on and off. For instance, hot hotter days, the cooler you set your AC, the more the compressor has to work to maintain the desired temperature. 

Once the desired temperature is achieved, the AC compressor may cycle off for a while until there is a change in your car’s temperature. Thus the air conditioning system cycling on and off is not a problem, but the frequency of cycling might indicate problems. 

An example of such abnormal cycling frequency is that instead of cycling on and off, the AC compressor stays on all the time.