A thumb ring is a symbol of wealth and influence in many societies. Such rings tend to be large or slightly bulky to reinforce their symbolism. They typically are not extravagant, gaudy or overly expensive in appearance.
It doesn't matter on which hand a thumb ring is worn. Because the thumb is often associated with goodwill, social interaction and friendship, wearing of a thumb ring can also indicate a person's character. It also frees up space on the wearer's hand if the person wants to wear multiple rings. Due to the space between the thumb and other fingers, it keeps the hand from looking cluttered by wearing too many rings.