Originally a Varial was a Frontside Air where the skater reached between the legs and grabbed the board on the heel edge with the back hand (now known as a Roastbeef grab), then turned the board 180 degrees frontside with the hand before putting it back on the feet and landing. Like all Frontside Airs at the time, they were performed without an Ollie (early-grab). This version, however, is not very common anymore. Tony Hawk invented the Backside Varial in the late 80s, adding an Ollie in the process. Before long, 360 Varials, where the skater turns the board 360 degrees backside and grabs it, became commonplace. After the invention of the Kickflip Indy, most professional vert skaters had to be able to perform one to win a contest, and soon they were looking for ways to increase the difficulty. One of the ways was to spin the board 180 degrees during the Kickflip, which ended up being called a Varial Kickflip Indy. Somehow the term filtered back in to street skating and it became common for a Kickflip combined with a Pop Shove it (180 spin of the board) to be called a Varial Kickflip. Some have even gone so far as to drop the "kickflip" from the name altogether, calling a Kickflip Shove-it a "Varial." However, vertical skateboarders still use the term Varial to describe any trick involving spinning the board and grabbing it.
Source: wikipedia