Famine's ring is a ring that helps the Black Horseman, Famine, channel and focus his powers. Without it, in the physical world, he is left, as the demon Brady puts it, a "withered husk". Sam and Dean obtained Famine's ring after Sam exorcised demons out of Famine's body.
When combined with the other three Horsemen's rings, it can open up a portal to send Lucifer back into his cage again.