Your Computer needs a clear flow of air to keep it cool. The fans are the method of creating that air flow.
All air contains dust and there will be a very gradual build up, but in most cases a cleanout every 3 years, or so, will do the trick.
However if you place the case unadvisedly you can make things much worse.
On the floor is a bad idea. Where the cat can sit on it, it's warm, is a really bad idea. In a cupboard, or any other enclosed space, makes the fans work overtime because it heats up in there. Using a laptop on your lap or on a blanket in bed is, plumb stupid.