The black dust cover keeps you from seeing the unfinished materials that your foundation is built from.
It also keeps out some of the dust, insects, pets etc. that would otherwise find their way inside.
The same type of dust cover is used on the bottom of most upholstered furniture. (Sleepers and most reclining furniture do not use dust covers.)
The purpose is so that your cats have somewhere to claw into and “nest”. Don’t be dull.