The sole function of an air conditioner is to remove warm air from the home and to replace it with cool air. In the process, the warm air is typically moist and humid, so when it’s replaced with cooler air, the humidity is also removed in the process.
Indoor air is moved over the refrigerant (cooling) coils of your AC unit and through the process of condensation, the heat is removed and the moisture exits the home via a condensation line. So, yes, air conditioning can effectively dehumidify your home; however, there may be circumstances where the AC is not enough.