Widely disputed as being a fake, there's actually a company responsible for making things like this!
According to the company website:
Zapata’s Flyboard Air EXP™ is the next generation of advanced individual mobility. An embedded stability program uses vectored thrust from six small turbine engines to create an intuitive, responsive, and imminently stable flying platform. Engineered for safety, the Flyboard Air EXP incorporates multiple redundancies to provide graceful degradation and safe landing in the event of control channel interruption or multiple engine-loss. With Zapata’s™ proprietary balance methodology, fail-safes, and patented designs, the Flyboard Air™ is superbly safe and stable in the air and can reach speeds of over 90 mph, allowing the user to fly with exceptional confidence.
They reckon it can go over 90mph, but you'd need balls of steel to fly this thing!
One false move and weeeeeeeee, splat...
They've even got a Guineas World Record for their efforts...
Seems pretty real to me!