Improper AC Size
Before turning to other alternatives as to why the air conditioner is not sufficiently lowering the house's humidity level, make sure that the air conditioning unit is sized properly to service the space you have it cooling. Install an air conditioner that is too small, and the unit does not have the power to either cool the area, or remove the humidity inside the room to a comfortable level. On the flip side, install a unit that is too large for the designated area, and it will cool the air and shut off before it lowers the humidity sufficiently. Match the space with the amount of BTUs, or British Thermal Units, the air conditioner has.
The AC Needs Help
If the house has an extremely high level of relative humidity, the air conditioner might need help in bringing the level down to between 30 and 60 percent, which is the range that you will find the most comfortable, and that will avoid damage to the house from excessive moisture. In this case, place a dehumidifier in the room. Just like an air conditioner's main purpose is to cool a room, the dehumidifier's responsibility is to remove the room air's moisture, and dehumidify it.
You're Constantly Adding Moisture
Even if the air conditioner is operating as it should, you might be adding additional moisture to the air inside the house, just by carrying out basic household activities. Hot showers and baths, for example, add moisture to the air, especially if you don't use the bathroom's exhaust fan to vent the room. Likewise, cooking adds moisture to the air, and you should use the oven fan to curb it. Make certain the clothes dryer vents to the outside, also, or it will add to the indoor humidity.
Drafts and Downspouts
If the outdoor air is hot and humid, and you have cracks around windows and doors on the house, the humid outdoor air might be slipping inside. Examine around the windows and doors on the interior and exterior, and seal any cracks and leaks with caulk. Also, make sure that the gutter downspouts around the house's exterior are properly directing water away from the foundation, so water won't be pooling in the crawl space underneath, which allows moisture to enter through the floor above it.