An aerial, or air step, is a dance move in which the follower loses contact with the floor. Aerials as such are not a specific dancing style, but due to
their dynamic character and because they are fun to watch, they are often used in Lindy Hop choreographies.

Here’s a famous Lindy Hop scene from the Hellzapoppin’ movie (1941), featuring one of the founding fathers of Lindy Hop, Frankie Manning. You can see lots of back flips and a super-fast Lindy flip (a kind of swing out in the air, 1:48).