Amnesia is a medical term that refers to a loss of ability to retrieve memories relating to things like facts and experiences; though the Mayo Clinic indicates that it's theoretically possible that a total loss of personal identity could occur in real life, such cases are extremely rare. In the real world, amnesia is much more subtle than the film "Memento" makes it out to be, and amnesia sufferers are usually only missing certain abilities related to memory, such as the ability to learn new things. There are multiple approaches to treating amnesia, and while there is no specific cure for the condition as a whole, taking the "Memento" approach of tattooing information on one's body isn't an accepted medical solution.
One of the main things that "Memento" gets wrong about amnesia is that it includes a total loss of personal identity. Typically, the loss of identity is associated with other psychological or neurological conditions. Instead, amnesia is an inability to form new memories or recall past memories, but this isn't usually as dramatic an inability as it is depicted in fiction. There are also other conditions, such as dementia, that can cause memory loss. Amnesia is typically caused by trauma such as head injury, though there may be other factors in play.