As you have not specified much detail of your air conditioner, we can give you a brief knowledge on how the controls function depending on the manufacturer variants of the units you have.
The ON/OFF Compressor Control
The compressor is one of the most important components of the vapor compression- refrigeration system of the AC. So, the ON/OFF feature would differ with the type of compressor you have. for example, if you have a DC Inverter type of compressor, then the ON/OFF feature of the compressor will work depending upon the temperature you have set and also on the ambient temperature. If you have kept it on cooling mode, the compressor will turn ON automatically.
Setting the Mode will define the functionality
There would be a button in the remote control that would allow to set the mode of operation for the AC.
It would generally have 3 basic modes. a) COOL b) HEAT and c)DRY mode,
But it would also have the AUTO mode and a FAN mode. You need to consult the user manual to know the symbols for each.
If you have turned on the AUTO mode by any chance it would automatically keep changing between the COOL and HEAT modes with the help of its temperature sensors and would adjust the temperature of the room to a moderate one.
In almost every air conditioner model, depending upon the brand of manufacturer, the AUTO mode would be start operating first in the COOL mode with a lower temperature to quickly cool down the room before the next set of instructions are given. So, it is natural for the Inverter type ACs to go for On/Off modes automatically.