The sanding of coats in-between is to give the new coat something to adhere to. It roughs up the surface just enough to give it a bit of grip.
Multiple coats is the same as anything else. Multiple coats makes the coating thicker, stronger and more lustrous.
Cars have multiple coats of paint to protect the body; you paint your walls with multiple coats to ensure even coverage; you poly furniture with multiple coats to ensure durability.
Don't sand to much. Use a very fine grit and just rub over it. The grit should feel like loose leaf paper. You'll have white dust when your done. Make sure to wipe the piece very well with a soft cloth before applying the next coat.