Amnesia, is a form of memory loss in which a person loses some or all recollection of themselves and their past. In video games, it is a commonly used plot device in which the premise is set-up by way of the player taking control of an amnesiac protagonist.
Developers use this conceit to explain who the character really is throughout the story without having to use a lot of exposition up front. Over the course of the game, the protagonist's memory is either restored piecemeal or all at once, filling blanks in the story.
In reality, there are different forms of amnesia. Retrograde amnesia is the form most commonly depicted in fiction; patients that suffer from it have lost their memory of some or all of their past. Anterograde amnesia, on the other hand, inhibits the patient's ability to create and retain new memories. Their minds in essence continually reset to a state in which they cannot remember anything beyond a specific point in their lives.
Examples in Video Games
Psychic City / Hoshi wo Miru Hito
In the 1984 cyberpunk role-playing game Psychic City, and its 1987 NES console remake Hoshi wo Miru Hito, the protagonist is a psychic who has no memory of who he is. He soon discovers that he, along with other fellow psychics, are being pursued, due to the city's inhabitants being brainwashed into believing that psychics are a threat to humanity. It is later revealed that a supercomputer has been controlling the minds of the city's inhabitants and is intent on capturing psychics.
Deja Vu: A Nightmare Comes True
In the 1985 graphic adventure title Deja Vu: A Nightmare Comes True, the player character starts the game off by awakening in a toilet stall with his memory completely wiped. He soon finds himself embroiled in a murder mystery, in which he appears to be a prime suspect. When he finally regains his memory, the protagonist remembers that he is Ace Harding, a private investigator, and he had been drugged into an amnesiac state and framed for the murder.
In 1986, Squaresoft's cyberpunk adventure / visual novel game, Alpha, added its own twist to the amnesia trope: amnesiac immortality. In this case, the amnesiac character in question doesn't remember her identity, but believes herself to be human, before a twist ending reveals that she was in fact an android who had been created centuries ago. The concept of amnesiac immortality would later be used more extensively in games such as Glory of Heracles III (whose writer Kazushige Nojima later wrote Final Fantasy VII), Planescape: Torment, Shadow of Memories, and Lost Odyssey.
The Magic of Scheherazade
The 1987 NES role-playing game The Magic of Scheherazade begins when one day a mass of demons suddenly attack Arabia at the evil magician Sabaron's command. The hero attempts to stop the assault, but fails miserably. As a result, his sweetheart Scheherazade is taken from him, he is flung into a different time period, and his memories are erased. With the help of his guide Coronya, the hero goes on a quest to regain his lost memories, return to his time period, and rescue Scheherazade. When he eventually regains his memories, he realizes that she was never kidnapped, but was accompanying him all along disguised as Coronya.
Final Fantasy VII
In 1997, Squaresoft's most famous game, Final Fantasy VII, inverted the amnesia trope. Instead of the usual formula of having a character attempt to discover their identity, the game instead concealed the fact that the character suffers from amnesia for much of the game. In this case, Cloud doesn't realize that he suffers from a false identity disorder and partial memory loss, up until a major plot twist in the second half of the game. Furthermore, it also inverted the usual trope of an involuntary, physically-caused amnesia, instead being a voluntary, denial/trauma-induced psychological disorder, in some ways anticipating twists later seen in games such as Metal Gear Solid 2 and Shadow of Memories or films such as Memento and Shutter Island.