Until 20 minutes ago, I'd never heard of Danny MacAskill, and, despite a long history of international bike trips, I'd never heard of the sport "bike trials" either.
The site biketrials.com isn't positive how the name came about but explains the sport this way:
Bike trials is a sport in which one's bike skills are tested. They are tested through a series of sections, or trials.
Bike trials practitioners lose points if any part of their body touches the ground during the trial. But that's only part of it. It's a precise and beautiful endeavor -- and it's on a bike. MacAskill apparently has some kind of celebrity endorsement with Remington. They present this short, slickly produced film/commercial, shot in San Francisco.
FYI MacAskill's Scottish brogue is compelling if not entirely intelligible.