Also known as air-steps, these are the high-energy, high-athleticism lifts, flips, and other airborne signature moves of swing dancing, specifically Lindy Hop. They were made popular during the 1990's swing revival by the movie, Swing Kids, and the mid-1990's Gap khakis ad (tagline, "Khakis Swing").
Their creation, or at least introduction, into Lindy Hop is attributed to swing-great Frankie Manning. As the story has it, some time in the early 1930's, Frankie and his partner at the time were practicing for the Harvest Moon Ball at the Savoy Ballroom. They were looking for an edge to defeat the then champion "Shorty" George Snowden. After several bruise-inducing weeks of practice in Frankie's apartment with mattresses on the ground to break their falls, Frankie and partner busted out the world's first aerial to the delight of the crowd at the Savoy and stole Shorty George's crown.
For a good idea of the state of the art in aerials in Lindy, circa 2000, check out the Broadway musical, Swing!, or the competition routines of Yuval Hod and Nathalie Gomes and their Hop, Swing, and a Jump competition team.
The general consensus in the Lindy community is that aerials are more for competition and jam circles than social dancing. The high level of athleticism required make them difficult, if not outright dangerous, to execute on a crowded dance floor, especially with a partner you have just met. Because they are pretty darned cool, however, newbies always want to know when they're going to learn how to "throw their partners around". But that's before they know they can reach a perfectly good Lindy high without any aerials at all.