Using cardboard to prepare soil for planting is a form of sheet composting. Theoretically you have soil layered with a type of vegetation you don't want. The cardboard will turn the vegetation into humus and prepare your soil for planting. In this area,the hot and humid South, by the end of summer the cardboard has disintegrated and all you have is soil and the former vegetation turned into humus. By then I have planted what I want in the spaces between the cardboard, or through holes punched in the cardboard. And I may even add more cardboard to mulch around my new plants.
The Gulf Coast area where I am is sometimes call "subtropical". I have a lot of vegetation and my soil is quite fertile -- so it grows a lot of vegetation that I don't want. The cardboard turns the unwanted vegetation it into soil that I can use to grow what I do want. Some people don't like the look of cardboard, so they cover it with mulch of some kind.
If your soil is not good and you want to add manure or compost, I would put it under the cardboard. I don't see the point of adding soil over the cardboard. Its sole purpose is to deprive the underlying vegetation of sunlight, so that it will disintegrate. The cardboard will also disintegrate. Adding more on top of the cardboard would seem to me to slow down the process.
However, if there is wind you may need to keep the cardboard from blowing away. And, as I said before, somepeople don't like the way cardboard looks, so they put something on top of it that looks better to them.
