I suppose the first thing they do is help us define any living animal with feathers as a bird. I'm trying hard now, in my mind, to prove myself wrong and think of a feathered animal that's not a bird, but I can't. Please let me (and the Natural History Museum) know if you can...
Feathers are a bird's insulation, they form a protective shield to the skin and they play a huge part in external appearance - which of course makes bird ID easier for us and makes spotting males and females easier; however, a feather's colour and pigments are as they are to assist courtship and amplify (during courtship) or camouflage (from prey).
It's a lot more complex than that but, that's roughly what a bird's feathers are for.
How often should we feed the birds? News from the bird table