Hyperthymesia

Hyperthymesia, also known as piking or hyperthymestic syndrome, is a condition where the affected individual has a superior autobiographical memory. "Thymesia" comes from the Greek word θύμησις thymesis, meaning "memory". As first described in a 2006 Neurocase article entitled "A case of unusual autobiographical remembering", the two defining characteristics of hyperthymesia are "1) the person spends an abnormally large amount of time thinking about his or her personal past, and 2) the person has an extraordinary capacity to recall specific events from his or her personal past. Hyperthemsics are capable of remembering the details of any date chosen at random, including who they saw, what they ate, and what events happened at that day. It appears memories start to form in this manner at the onset of puberty.
Nadia, the patient in You Must Remember This, had hyperthymesia. 
Hyperthymesia appears to be exceedingly rare, with fewer than ten confirmed cases in the United States. However, the condition has been well verified. One of the most famous people who has been confirmed with it is actress Marilu Henner.
Hyperthymesia at Wikipedia