Cutie Marks are images located on a pony's hindquarters.
Cutie Marks have existed in some capacity since Generation 1. They were originally called "Rump Designs", and only gained the "Cutie Mark" name in Generation 3.
In Generation 4, the TV series said that a pony's destiny is linked to their cutie mark. Many of the episodes and occurrences in the show were centered around cutie marks and their meaning to ponies. In Generation 5, ponies only have a Cutie Mark on their right side.