What is the origin of the title "Ghost in the Shell"? The anime series Ghost in the Shell has a Japanese name which can be transliterated as "Mobile Armored Riot Police"; from Wikipedia:


  Ghost in the Shell (攻殻機動隊 Kōkaku Kidōtai?, literally "Mobile Armored Riot Police")


It's clear to me that the English name of "Ghost in the Shell" is far, well, cooler than "Mobile Armored Riot Police". But why was this particular name chosen? What are its origins, and what significance does it have in the series (if any)?
Within the show, the word  "Ghost" is used to refer to someone's consciousness while a "shell" is the cybernetic body, much like the situation with Major Kusanagi. The Wikipedia page Philosophy of Ghost in the Shell has a lot of insightful concepts to add to this:

Referring to the Laughing Man and Puppet Master:


  Yet, as those criminals are revealed to have more depth than was at first apparent, the various protagonists are left with disturbing questions: "What exactly is the definition of 'human' in a society where a mind can be copied and the body replaced with a synthetic form?", "What exactly is the 'ghost' —the essence— in the cybernetic 'shell'?", "Where is the boundary between human and machine when the differences between the two become more philosophical than physical?", etc.


More specifically with the original film, there's this article:


  The director has the main character state “Who am I?” The Major, the Main character, wonders if she is a real person or a program. "Major Motoko Kusanagi barely exist in her original human form, retaining only a small portion of organic grey matter inside an almost totally robotic, titanium body or"shell." (Dan Dinello, page 276, Anime and philosophy) The title of the anime supports this, “Ghost in the Shell” likely refers to the phrase “A shadow of your former self.” The main character has a cybernetic mind and body, which leads her to question her existence, whether or not she is still alive. If one states that the difference between a human and a machine is that the human has a soul, what then, is a cyborg, such as the Major? “


A lot of these concepts and themes are tackled within the manga/anime. 

See also, the in universe origins of the terms "Ghost" and "Shell". I don't know if these terms were invented by Masamune Shirow or if he borrowed them from SF tropes.