This superstition arose from the belief that magicians had the power of imprisoning demons in rings. The power was supposed to prevail in Asia, and subsequently in Salamanca, Toledo, and Italy.
Magic circles (like magic squares) are mathematical puzzles.
“`This ring,' said Dame Liones, `increaseth my beauty ... That which is green it turns red, and that which is red it turns green. That which is blue it turns white, and that which is white it turns blue. Whoever beareth this ring can never lose blood, however wounded.'” —History of Prince Arthur, i. 146.
“Take this ring, and put it on thy finger, with the stone inside thy hand, and close thy hand upon it. As long as thou concealest the stone, the stone will conceal thee.” —The Mabinogion (Lady of the Fountain).
Reynard's ring. The ring which Reynard pretended he had sent to King Lion. It had three gems: one red, which gave light in darkness; one white, which cured all blains and sprains; and one green, which would guard the wearer from all ills, both in peace and war. (Henrik von Alkmaar Reynard the Fox).
The steel ring, made by Seidel-Beckit. It enabled the wearer to read the secrets of another's heart. (Oriental Tales; The Four Talismans).
The talking ring given by Tartaro, the Basque Cyclops, to a girl whom he wished to marry. Immediately she put it on, it kept incessantly saying “You there, and I here.” In order to get rid of the nuisance, the girl cut off her finger, and threw both finger and ring into a pond. (Basque legends.
This tale appears in Campbell's Popular Tales of the West Highlands (i. to iii.), and in Grimm's Tales (The Robber and his Sons).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Magic Rings from Infoplease: