Down is the stuff from baby birds before they get feathers. It's very insulating and that's why it's so good to use in comforters and duvets. However, many people are allergic to it. Down-alternative is a completely man-made, synthetic product that acts like down, except that it's allergy-free.
I'm not 100% sure but I'm guessing down would be real feathers and down alternative would be some thing like real down but not actually real down. Kind of like buying something from a Louis vuitton store for 1000$ (down) and getting a knock off version for 20$ (down alternative)
Down is real feathers. Down alternative could be man made materials or different types of feathers mixed with man made materials. One is expensive and one is not as expensive but is not the real thing.