The secret to their stealthy movement lies in the design of their feathers. When air flows over a typical bird wing, turbulence is created, causing a rushing sound. Most bird feathers are stiff and rigid with almost pointy edges. When air hits them, turbulence is created, causing sound.
Owl wing feathers have several ingenious designs that greatly reduce sound, especially when the wing tilts as the owl nears its prey. The leading edge of the owl's wing is covered with tiny comb-like structures that break up the incoming air into many micro pockets of turbulence. Those smaller gusts of air then flow over the owl's wing to the trailing edge which is made up of a soft fringe and separates or muffles sound even further. Any remaining sound is absorbed by the downy feathers on the owl's legs and wings.
Owl wings are also larger and wider than the wings of most birds of prey, which gives them more lift so they don't have to flap as often. Their large wings make them slower, but the combination of size and unique feather features create the perfect design for the nocturnal owl.
Check out these amazing videos which demonstrate the silence of owl flight when compared to other birds.
BBC - Super Powered Owls
KQED - See What Makes Owls So Quiet and So Deadly
Reference and Resources
Ask Nature
Image - Public Domain Pictures