Floors are basically the part of a house that is meant to be walked on. Without floors, most people would just walk on dirt, concrete, or pipes. Luckily, floors help prevent this from happening. Floors can be covered in carpeting to make them softer, or they may be made of tiles or hardwood. Hard wood.
The King is obsessed with getting them scrubbed, but usually refuses to scrub them himself. He often punishes his enemies by making someone scrub them, most infamously Duke Onkled.
Originally, Duke Onkled was meant to scrub all the floors in every single house, building, and non-building in Hyrule. However, considering that would take far too long, and that all the floors would just get dirty again before they were finished, the sentence was changed to Duke Onkled having to scrub all the floors in Hyrule Castle for the rest of his life instead. (He will also scrub Gwonam's floors on occassion, as well.)