Alzheimer's disease, often just known Alzheimer's, was a neuro-degenerative disease which prior to the 23rd century affected older humans mainly over the age of 65. The disease was characterized by progressive cognitive deterioration, along with a decrease in activity, and behavioral changes.
Sometime prior to 2286 medical science had cured Alzheimer's. When Gillian Taylor asked the Admiral James T. Kirk if Alzheimer's disease had been cured by the 23rd century, Kirk had not even been aware of the existence of the disease. (TOS novelization: Star Trek IV: The Voyage Home)