The character suffers from some kind of amnesia (memory disturbance or loss). This may mean inability to memorize new information, or inability to recollect old memories. Since there are many types of memory, the person may e.g. forget who they are but still retain learned skills.

Amnesia is fairly common in fiction as a plot device. In fact, because it allows for major plot changes while requiring little creativity from the author, it may be subject to heavy overuse.