I made the paper with thick card stock paper. 4 inches (10cm) by 2 inches (5cm). Bend the paper on two slides down. You can try bending the paper shorter or longer to see if you get a better lift.
When you spin the piece of card, it moves through the air like a wing. As the air hits the flaps, it is forced downwards. Isaac Newton worked out that if you push something one way, it will push you back; so the card pushing the air downwards means that the air pushes the card upwards.
Essentially you have built a rotating wing. The wing is moving through the air even if the card doesn’t stays over the same place, therefore it can hover.
This is exactly the same principle as a helicopter, but a helicopter has added problems. Because its engine is always pushing the rotor blade around, the equal and opposite force should cause the helicopter to spin in the opposite direction. This is why helicopters have to have a tail rotor to provide a balancing force.