A bit of a complicated subject but the short answer is you're correct humidity does reduce the efficiency of air conditioning.
The reason why(/long answer) is that as it cools the air the humidity in the air (i.e. water vapor) will condense into liquid water. Water requires a fair amount of energy to be removed (known as latent heat) to make this change and none of that energy removed actually changes the temperature of the air (all of it goes into changing the phase of the water). Therefore a high humidity load results in a lot of the cooling potential getting "used" up removing humidity first.
The reason why(/long answer) is that as it cools the air the humidity in the air (i.e. water vapor) will condense into liquid water. Water requires a fair amount of energy to be removed (known as latent heat) to make this change and none of that energy removed actually changes the temperature of the air (all of it goes into changing the phase of the water). Therefore a high humidity load results in a lot of the cooling potential getting "used" up removing humidity first.