Yes, an air conditioner removes moisture from the air. It dehumidifies the indoor air by removing both heat and moisture. Excess condensation drains out of your unit through the condensate pan. It is behind the evaporator coil. This is after the refrigerant absorbs the moisture and warmth from the indoor air. So, in response to your question, your air conditioner does indeed remove humidity!
Check out our best pick dehumidifier LG Air Conditioner 22000 BTU.