Xue Sheng hits the point on the head.
If we're talking about the typical "trinity" cited in many Asian martial arts, the majority of the discussion of "spirit" in this thread have been completely off the mark.
Indeed, I think the "body, soul/mind, and spirit" trinity is definitely a western concept. Not solely western, but the division can be traced back to the renaissance with regard to martial arts.
I attended a seminar a month or two ago about Thibault, a fencing master from the 1600's. Most of his style is integrated with his personal philosophies, so to understand his style, it helps to be familiar with his frame of mind.
The instructor brought up the idea of body, mind, and spirit, or, to be more accurate: spirit, mind, and body. If I remember correctly, the philosophy was that the body was driven by the instinct, the "Animus" (animal nature?) was the term he used. It wasn't so much the motions of the physical body (though that is certainly part of it) but the motivation of the body.
An untrained fighter will be "controlled" by the body, or the "animus." The overcommitment to actions, primitive reactions, the emotional responses, the tendency to panic, etc. This will influence how the mind perceives the situation, and the mind is now controlled by the body. The mind then controls the "spirit," in this case, the will to fight. The will is lost, and the fighter will give up easily.
A trained fighter will be controlled by the "spirit" -- that is, according to the teacher's interpretation, the certainty of know that what you are doing is "right." There will be no hesitation because you are acting in full accordance with your beliefs. In the case of Thibault, that would mean that you are acting in accordance with "Divine Will" (enter the religious part.) Whatever your religion doesn't really make a difference, as long as you are able to fully believe that you are morally justified in commiting violence against another person. If that "spirit" is in alignment with your religious beliefs (whatever they are), then your mind will be empowered to pursue those beliefs. With the mind/soul, thus empowered, it is able to control the body, and use it as a servant to the "spiritual" desires. You are able to overcome the primitive desires of the body, and perform better, calmer, and longer.
Now, this is from memory, and is my interpretation of the interpretation of the instructor. But the reason it stuck out to me is that it parallels some of my basic theology. This isn't surprising, because Thibault was influenced by Christianity, and I am a Christian, so yeah.
According to "tricotamists" who believe that we are divided into Body, Soul, and Spirit, the condition of those who have not been "born again" is the same as the description of the untrained fighter, above. The spirit is weak, sick, or completely dead, leaving the primitive desires of the body in charge of actions. These are selfish desires, and usually result in selfish actions. The body's desires control the mind, which is then used to provide the body with what it desires.
The "born again" person refers to the rebirth, or awakening, of the "spirit" which, over time, begins to take control of the person, eventually using the mind to control the body. Of course, the more "mature" or in control your "spirit" is, the closer you are to God. The closer you are to God, the more power the spirit has, since the spirit recieves it's power from God. This often what people refer to when they talk about the "Holy Spirit" -- that is, the spirit that is the connection between our body, soul, and God.
Not to get preachy, but this is the "philosophy" section.
But that is why I believe that the original idea of "spirit" in this thread, and in fact the idea of "sprit" in general in the west, is a cultural thing influenced by the christianity of the west, not so much by the philosophy of the east.