With the sun behind you, only those water droplets that have the same angle formed by you, the drop, and the sun (this angle happens to be approximately 42 degrees) will contribute to the rainbow. Other droplets send their light somewhere else, and if you move to a different location, new droplets are needed to make the rainbow you see in the new location. The rainbow is curved because the set of all the raindrops that have the right angle between you, the drop, and the sun lie on a cone pointing at the sun with you at one tip.