What is a powered parachute?
A picture is worth a thousand words - so, click on "PPC Pictures" to see them. But, it is a carriage (some people say a lawn chair), an engine (some people say a lawn mower engine), and a wing made of fabric (some people call it a parachute).
It's pretty much magic. OK, it's simpler than that. The cells of the chute are inflated by the forward motion of the carriage, and the floppy piece of fabric becomes a sort of rigid wing. Here's the magic part - then it becomes a real airplane. It flies at a constant speed of about 26 mph - you can't fly it slower or faster. In the hands of of a trained and experienced pilot, it can be flown as precisely as any other aircraft.
Cheap - at least compared to other aircraft. about $15,000 for a two seat unit, about $11,000 for a single place. Hangar it in your garage or trailer. Pay about $400 to $500 for lessons. Another $300 or so to get your FAA license. Then go out and enjoy a most exquisite and unique experience of your life - flying in the open, with nothing around you. See things you could see no other way. Fly like a bird.
What is its legal status?
Single seat powered parachutes (if they meet the requirements of 14 CFR Part 103 - under 254 lbs, 5 gallons of fuel, etc) do not have to be registered, and can be flown without a license. Two seaters are classified as LSAs (Light Sport Aircraft) and have to be registered like all other US civil aircraft. You need an FAA pilot's license (Sport Pilot or higher) to fly them. See the other sections for more information on that.