The diamond cocktail ring is meant to be a dramatic large ring, worn at cocktail parties. The cocktail ring was especially popular to wear during US prohibition at illegal cocktail parties. Such a ring flaunted not only the fact that one was drinking illegally, but also that one was doing it with style.
Popularity of the cocktail ring gained in the 1940s and 1950s, as cocktail parties continued to be popular events. Although cocktail parties are less common now, wearing a cocktail ring with huge diamonds or other large precious or semi-precious gems is still popular for formal dressy occasions.
The diamond cocktail ring may be worn on any but the ring finger of the left hand, which represents that one is married or engaged. The right hand ring finger is often chosen, though the ring may also be worn on the index finger. Dismonds-USA.com