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.