Perhaps it's time we had a thread about this. The first videos a few months ago were designed to look as though they'd been faked: the idea was to gain publicity by stoking conspiracy theories on the internet.
As more and more videos have been released and they now have an official Guinness world record and Vodafone as sponsors, almost everyone now accepts that it's real.
It uses four gas turbines (the sort of jet engines sold for model planes) to provide the downward thrust, and two battery-powered electric ducted fans (again model plane components) to provide yaw (twisting) control. The fuel for the jets is contained in the backpack that the pilot wears - the jets are thirsty so it can only fly for about five minutes.