A ‘feathered’ friend is a bird — any bird kept, fed or simply befriended by a person. The phrase is an example of synecdoche: one striking feature, the feathers, is used to stand for the whole creature.
It could be a pet budgerigar or canary in a cage, the sparrows and mynas that come to a windowsill for grain, the crow that waits on the terrace wall, or a pigeon a family has raised. In this unit the ‘feathered friend’ is Claribel, a small yellow canary living on a space station.