The floor is actually a piece of matter that fits snugly into the cubic tile. Dwarves and other creatures that live can pass through it horizontally but if they try to do it vertically, Urist has a heart attack. So they avoid doing that.
Oh yeah, almost forgot. IT HAS EVERYTHING TO DO WITH BEARDS!
Exactly... The floor takes up the entire tile. If there's an upward stairway sitting on that tile, you cannot place a floor on that tile without moving the stairs out of the way. Imagine that you built or carved some upward stairs out of a sandy clay loam wall. There are stairs in the tile, and whatever portion of the tile doesn't have stairs on it has sandy clay loam floor. If you want to replace that floor "beneath" the stairs with something else--say, lovely cinnabar blocks--you can't just nudge it through the stairs, and you can't shove it under them, because the stairs were carved out of the existing wall and they are attached to the floor. Think about it, you can build up stairs over a gap because they have a chunk of floor attached to their underside. Dwarves can stand on the landing. Stairs support tiles above them and suspend tiles hanging below them.
Here's a drawing so you aren't confused by anything except my awful MSPaint skills:
The upper left is my lovely cinnabar block floor. As you can see, it is 1 tile wide by 1 tile long by floor-width high.
The upper right is a downward stairway carved from sandy clay loam. As you can see, the tile is still 1x1 and floor width, but it also extends downard to meet with the upper limit of the tile below it. However, as nothing is occupying any of the space above the stairs or the 'partial floor tile' surrounding them, you can easily build a cinnabar block floor that covers both the down stairs and the floor attached to it, and later remove that floor to reveal the stairs and the original floor.
The lower left is an up stairway, also carved out of loam. As you can see, it's also 1x1 with a floor attached, but it has a stairway extending upward from floor level which occupies the tile's z-height up to the lower limit of the tile above it, allowing you to connect floors. Note that this stairway is built on top of the artificial floor that it's attached to, giving it a landing. You could not place a cinnabar block floor neatly over that artificial flooring without removing the stairs, because they are in the way and will not politely scoot aside will you floor them. In fact, you cannot build a floor and an up stair in the same tile, they NEVER coexist, either in constructions or natural rock or soil or ice or metal bars or anything else. Note that you CAN build an upward stairway construction on top of a natural rock or soil floor, but that doing so would remove any smoothing or engraving on that tile--just as if you placed a wall or floor on the tile and dug it up, because the up stair has its OWN flooring.
Lastly, in the lower right, we have an up\down stairway. All facts about the up stairway and down stairway apply here as well, except that once you treat the tile like a downward stairway by doing something to it that can only be done to a downward stairway (flooring over it), it ceases to be an up\down stairway because the upward portion was removed to make room for the floor which then covered the downward stairway.
####/####
####\####
####/####
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Imagine this as a 1x by 1y by 4z staircase. Each tile of \ / is an up\down staircase. Now place a floor on ANY tile in this staircase:
####/####
####_####
####/####
####\####
Oh shit. Makes sense now, doesn't it? The floor perfectly seals off the stairwell, and occupies the space that the up stairway and its landing would have occupied. A "(b)(C)(f) Floor" in dwarf fortress is a 1x1 tile of smooth, uninterrupted stone flooring without holes or crap on it.