"You've learned Climb! To use this ability, press and hold RT (Shift) when you're against a wall to travel along its surface!"—Ori and the Blind Forest
Climb is the 8th skill Ori learns, obtainable in Misty Woods. It allows them to climb along vertical surfaces, while also recharging their double jump, and allowing them to leap off and grab onto another surface.
Press and hold Shift (RT/R2 on consoles) while on a wall to grab onto it.