Abarim Publications' online Biblical Greek Dictionary
The noun πνευμα (pneuma) is used 385 times in the New Testament, see full concordance, and is generally translated with the tainted and over-abused word "spirit". Sensationalists and book sellers will try to make their audiences believe that our spirit is a part of us, or some wavy kind of energetic reflection of our being, but that's false (to use a kind word).
In our New Age world there has been as many lofty attributes assigned to the spirit as to Chuck Norris, but the truth of the matter is that all "parts" of you are physical, and thus part of your body. Your πνευμα (pneuma) is a mental or behavioral function and is not an independent element of your being.
Spirit and soul
The spirit is often mentioned in tandem with the soul, which is another commonly misunderstood concept. The Greek noun ψυχη (psuche) comes from the verb ψυχω (psucho), meaning to breathe, or rather to draw breath, and very simply denotes a living thing that draws breath — and the "breathers" are obviously a subset of the larger world of living things (known by the word ζωη, zoe, life).
Contrary to pagan musings, when a person's breathing departs from him/her, it doesn't go anywhere, it just stops. But at the promised resurrection of the body (Mark 12:8-27, John 5:28-29, John 11:25, 1 Corinthians 15:1-58, Philippians 3:10) it returns — that is to say, the person starts to breathe again and becomes a living soul once again (see Genesis 2:7: "and Adam became a living soul"; he didn't get one).
Our noun πνευμα (pneuma) likewise comes from a verb that has to do with breathing (namely πνεω, pneo; and see our article on this verb to meet our noun's siblings), but this time the verb emphasizes a breathing out rather than in. The difference is colossal, because even though both inhaling and exhaling are part of the same process (namely breathing) and this very process demonstrates that a person is alive, the inhaling part is all about deeply needing something that you can get all around, whereas the exhaling part is about releasing waste products and the excess of stuff that you took for yourself but in the end had no need for.
And of course, onto our breathing-out we can piggyback a wonderful array of signals, from whistles and shouts to Psalms and Shakespeare and even scent-signals that tell our neighbors whether we are healthy or not. And that's the key idea of the spirit: the ability to bond with other beings (including God) and create the larger structures we call societies and cultures (see for instance Daniel 10:20). Likewise the Holy Spirit is not a part of God but God doing something, predominantly uniting people into what's called the Body of Christ.
Spirit is a word like electricity; it doesn't sit at some specific location and does not take on the personality of the one it moves. Spirit leads elements into a common direction, just like the wind that waves through a field of standing grain or scoops up piles of leaves and makes them dance like birds in the air. Flocks of starlings or schools of fish operate on the spiritual principle, and so do bees and ants.
It may be a bit of a let down for people who believe that incense, rainbows and healing crystals are "spiritual things", but no, there are no "spiritual things" and all spirit is willful interaction and cooperation. Our cities are highly spiritual, but so of course is our language. It's taking eons of interaction and forming agreements to produce the language we use today, and there is very little on earth that is more spiritual than language (apart perhaps from the Internet).
The Biblical spirit
The Greek in which the Bible was written made no distinction between upper and lower case letters, so it's not always clear when the Bible speaks of the Holy Spirit or a human spirit. In John 6:63, for instance, Jesus says that the spirit gives life, and for centuries commentators have wondered whether this speaks of any man's spirit or the Spirit of the Creator.
The solution comes when we abandon the idea that a spirit is some individual entity and recognize our word πνευμα (pneuma) as to describe a function within the mechanism of creation, whose effect it is to federate individual elements into a working co-op, and at every possible level.
Spirit is the mutual engagement of atoms into the formation of molecules and objects. It's the forming of colonies from organisms, cultures from humans and ultimately the formation of the Internet and the Body of Christ — which, we'll coyly add, is like a baby that grows in the womb of its mother, namely our world. All the world sees of this Body of Christ is the placenta that divides their two economies, which is probably the visible church, its buildings and institutions. But behind this wholly worldly facade sits an utterly new form of humanity that the world can not imagine to exist.
When one gives up the spirit (Luke 23:46, John 19:30), the bonds between the person and general humanity is severed, and when one's spirit returns (Luke 8:55) this bond is restored. Upon his death, Stephen cried out to Jesus to receive his spirit (Acts 7:59), which means that Stephen lost his bond with humanity at large and became solely connected to the Body of Christ.
A soul-driven person (in Greek: ψυχικος, psuchikos, usually erroneously translated with "natural") focuses on personal needs and desires, whereas a spirit-driven person (πνευματικος, pneumatikos, usually translated as "spiritual") is more concerned with the larger collective (both terms occur in 1 Corinthians 15:44).
Love, obviously, is the most spiritual act there is, and no greater love exists than to lay down one's soul-driven life for one's friends (John 15:13).