Silverware and jewelry are usually made of sterling silver, which is harder and more durable than pure silver. It can develop a dingy film over time and lose its shine. To restore its luster, silverware and jewelry must be periodically polished.
If toothpaste can clean and whiten teeth, it should be able to do the same thing for jewelry, right? Put a little toothpaste on your fingertips, then rub it on silver jewelry. Let it sit about 1 hour. Rub off with a soft cloth.