mid-13c., "recollection (of someone or something); awareness, consciousness," also "fame, renown, reputation," from Anglo-French memorie (Old French memoire, 11c., "mind, memory, remembrance; memorial, record") and directly from Latin memoria "memory, remembrance, faculty of remembering," abstract noun from memor "mindful, remembering," from PIE root *(s)mer- (1) "to remember." Meaning "faculty of remembering" is late 14c. in English.
I am grown old and my memory is not as active as it used to be. When I was younger I could remember anything, whether it had happened or not; but my faculties are decaying now and soon I shall be so I cannot remember any but the things that never happened. It is sad to go to pieces like this, but we all have to do it. [Mark Twain, "Autobiography"]
Computer sense, "device which stores information," is from 1946. Related: Memories.