Hi, B. Say hello to our old friend mildew. This is the same stuff that grows on your shower curtain--at least it does on mine.
Removing it is easy, just wash it off with household bleach (like Clorox) and a sponge. Use a scrub brush if necessary and wear gloves and eye protection.
Keeping it off is more difficult. Basically, it will grow in any damp place and the spores are in the air. Covering your outdoor furniture probably will not help since that keeps the humidity in. About the only thing that really will help is getting better ventilation. Putting the furniture where there usually is a drying breeze will help some.