91.155(a) sets the VFR minima for the various classes of airspace in general. Note that “1000ft above” means the plane must be 1000ft above the cloud, not vice versa as you wrote. Also, the visibility here is flight visibility.
91.155(c) adds the additional requirement of a 1000ft ceiling within the lateral boundaries of controlled airspace designated to the surface for an airport.
91.155(d) adds the additional requirement of 3 miles ground visibility within the lateral boundaries of the surface areas of Class B, Class C, Class D, or Class E airspace designated for an airport.
91.155(c) seems moot at first glance, since 91.155(a) requires you to stay at least 500ft below the ceiling in class C, D and E airspace and 91.119(c) requires flying at least 500ft above the ground, but 91.155(c) prevents you from using the “Except when necessary for takeoff or landing” clause of 91.119 or the “open water or sparsely populated areas” clause of 91.119(c) as a loophole. It also prevents you from using the “clear of clouds” requirement in class B from flying VFR with a ceiling of 500-999ft.
The regulations don’t give an official reason why they are written the way they are, but there is a reason we say “the rules are written in blood.” For any given regulation, think about how you are likely to die if you break it, and you will probably find at least one matching accident in the NTSB archives.
Finally, for ceiling, we find in 1.1:
Ceiling means the height above the earth's surface of the lowest layer of clouds or obscuring phenomena that is reported as “broken”, “overcast”, or “obscuration”, and not classified as “thin” or “partial”.