Note: This answer is rails 3 specific. For rails 4 and later, look at other answers here.
If you precompile on your local machine, then you can commit these generated assets into the repository and proceed with deployment. No need to compile them on production machine.
But it introduces a problem: now when you change source files (coffescript / scss), the app won’t pick up the changes, because it will serve precompiled files instead. rake assets:clean deletes these precompiled files.
In my projects assets are precompiled as a part of deployment. Capistrano makes it very easy.
Also, I never heard of rake assets:cleanup.