According to TheChurch Visible, by James-Charles Noonan, Jr. (Viking), the bishop's ring is a sign of authority. In the earlier Code of Canon Law clerics who were not bishops were forbidden to wear rings.
As a symbol of episcopal authority the ring first appeared in the third century. By 637 A.D. St. Isidore of Seville would write, "To the bishop at his consecration is given a staff; a ring likewise is given him to signify pontifical honor or as a seal for secrets."
According to Noonan, the bishop's ring would later also take on the symbolic meaning that he was wedded to the Church.
The cardinal's ring is given by the Holy Father at a Mass following his being named a cardinal.