In Ancient Rome spotting an eagle in the sky was considered a symbol of good luck and assistance from the gods, as this bird is very strong and a phenomenal predator, hence resulting as a very good auspicia, a sign of divine benevolence. Furthermore the eagle, aquila in Latin, was used as the official emblem of Rome and was the symbol of the Roman military, representing power and strength. It was also associated with the god Jupiter, the chief deity in the Roman pantheon. Each Roman military legion carried one eagle standard (aquila) and the loss of the eagle was considered a terrible omen. Standards were considered so important and their loss such a grave occurence that the military went to great lengths to recover them, sometime fighting battles just to recover them. This particular ring likely belonged to a member of the military elite.
To discover more about jewellery in the Ancient World, please visit our relevant post: Jewellery in Antiquity.