Things that are downy are very soft and fluffy. Babies are sometimes born with little tufts of downy hair on their heads.
A teenage boy who wants to grow a beard will be frustrated by the downy hairs on his chin, and you could also describe the feeling of a peach as downy. When you rip your winter coat, the downy feathers inside might start floating out behind you in a trail wherever you go. These are also known as down, or the soft feathers that typically grow on a young bird — this is the origin, in fact, of downy.