Different owl and photographer, but same Idea. Photo by Dave Heuvel
For those new to the group, they don't fall off due to the way their tendons are arranged. When they are relaxed, the tendons in their feet lock, holding them in place. They have to engage their muscles and do the equivalent of standing up to let them go.
If you haven't seen the mega post in talons, check that out here.
For just the tendon info, with some animations, click here.