Rings are a symbol. There are different traditions in many countries; many people in the western world, when they for instance marry, either exchange rings, or one gives the other a ring. They can be bracelets (a french tradition), or rings for the "Ring Finger¹". They can symbolise friendship (a Claddagh ring, that you are a member of some secret organisation (Freemasons), or that you graduated/attended from this particular educational institution (various).

Historically, the ring was a symbol of slavery, or belonging to someone, as in being married. Today they have come to mean fidelity. The shape of the ring also suggests eternity, the circle of life and what have you not.