A rug is something made of woven fabric that covers a floor. If your downstairs neighbor is complaining about the noise, try buying a rug.
A rug is smaller than a carpet, which usually covers a room's entire floor — rugs leave parts of the floor exposed. Some are thick and dense, providing a cushiony area for walking or sitting. Rug also informally means "wig or toupee," so you could say, "Did you see that guy's terrible blonde rug?" And if you want to pretend something didn't happen, you'll have to colloquially "sweep it under the rug," or hide it.