Wearing a ring of stealth gives you extrinsic Stealth. If polymorphed into a creature that is capable of eating jewellery and the ring is of suitable material, you may eat this ring and may gain Stealth as an intrinsic.
In 3.6.1 wearing a ring of stealth gives one of "You move very quietly" (barefooted), "You walk very quietly" (wearing boots) or "You float imperceptibly" (flying or levitating) messages. Removing the ring gives "You sure are noisy" message.
In earlier versions, a ring of stealth, unlike elven boots, does not give any special message to indicate that you are stealthy, making it more difficult to identify. To test if a given ring is stealth, you can check if putting on elven boots gives a message or if monsters in a zoo/graveyard/throne room wake you when you enter.