In addition to quiet flyer's excellent answer:
Owls have large wings in relation to their body size and weight. One might think that no, their bodies are quite large, but actually owls are kind of flullyfluffy flying feather balls: what you percieve as their bodies, is mostly air.
This leads to two things:
Low wing loading. Their large wings do not need to create as much lift per area unit as, say, with pigeons. This leads to less turbulence, which in turn means less sound. Because of low wing loading they also can fly with very little wing movement, also leading to less sound generation.
The fluffyness (infor lack of a better word) supressessuppresses turbulence in wing - body attachment area, and any other turbulence around owl body. This means, of course, less sound.
When combined with wing structure described in q f's answer, all these factors create a pretty much absolutely silent flight.
Check out this excellent BBC Earth clip comparing the sound different birds make when they fly, and why so.
As for the aplicability of these features in stealth aircraft, not likely, athough I strongly second PerlDuck's vote for fur covered wings on aircraft. The fact is, however, that there is no sense in making the wings or the airframe more silent, when the sound of the propulsion is orders of magnitude louder than any other part of the aircraft.
P.S. It's actually quite eery to encounter an owl in flight when it's dark. You can hear other birds when they fly in your vicinity, but owls, no, they just blast right by you totally silently, without a warning. They've scared me sh__less a couple of times out in the wild, and I'm pretty sure they enjoy it...