Well, when you dont feather an image, all the pixels are Sharp. Say, the color goes from Brown, then to Red, Orange, Yellow, and then white.. Or whatever. If you are to Feather that, (wherever, can be a section of the image), it makes it look better. How it does that, is it it takes it to light red, even ligher red, light orange, even ligher orange, etcetcetc. Its very difficult to explain, actually.. So I tried my best. ..Understand?
Feathering a selection basically adds a pixel buffer zone (that you establish by telling PS what the feather radius will be), making it so the selection contour now arbitrarily adds pixels to or subracts pixels from your selection within the specified radius. Feathering is usually used, as someone already mentioned, to blend stuff together, BUT, it should be used with caution because the results can look ugly as hell. For better blending, I'd highly recommend that you use quickmask mode instead.
Yes, it does the same thing to renders.. Again, people have diffrent opinions. Some like it, some dont. Personaly, I dont like it. I keep it sharp, and then the stuff in other ways; makes it look more proffesional.