To humidify is to make something more moist or damp. If you have a dry cough that's keeping you awake at night, you might want to humidify the air in your bedroom.
Humidify means "make humid," and humid, or "damp," comes from a root meaning "wet." You could say that your long, hot shower is sure to humidify the air in the bathroom, or that you try to humidify your house in the winter by putting a pan of water on the wood stove. Possibly the best way to humidify a space is to use a humidifier, a small machine that adds moisture to the air.