
A litter box cover keeps stray litter inside the litter box. When cats use the box they scratch and push the litter around to bury those treats, and it is a good thing they do. In the process a lot of litter is moved around and not just big pieces. Dust is created that can settle over anything around it. A cover keeps the dust and the flying litter in the box.
A littler box cover is included with most litter boxes. They are connected to the box either with snaps or clasps or it merely sits on the rim of the box held firmly in place by gravity allowing for easy cleaning access. Most have vents in the top of the cover that has an odor absorbing material to keep things smelling pleasant, or at least not as stinky. Regular cleaning has the best affect on smell.
Many a litter box cover has a door as well further sealing off any unpleasant smells. One common mistake is to attach the door in the wrong direction, either locking the cat inside the box once they enter, or not allowing them to enter at all forcing them to do their business somewhere else, like a fresh clean towel. Keeping a litter box clean is the best combat for foul smells.