What is the difference between the spirit and the soul?
That is a very good question, and one that has plagued scholars for years. I will give you my ideas on it, based on my study of the Bible. I am not fluent in biblical Greek or Hebrew, so I will not base my answer entirely on the translations of those languages.
The first thing we need to understand, though, is that the words often translated "spirit" are the same words sometimes translated "wind" or "breath." Thus the first example of the difference between the two may be found in Genesis 2:7: "And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul."
Based on this, we can say that the spirit is the life force in us and the soul is the part of us that lives on after the spirit leaves us. However, this is not the only scripture that mentions either the soul or the spirit.
Sometimes the two words are used almost interchangeably. Thus in Job 7:11 they seem to mean pretty much the same thing. "Therefore I will not refrain my mouth; I will speak in the anguish of my spirit; I will complain in the bitterness of my soul." "For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart." (Heb 4:12) I think that even this passage is saying that, at least in a living person, there is hardly a distinction between the two.
Add to this the expressions "the Spirit of God," or "the Holy Spirit." God does not die, but he has a spirit. In this case, and perhaps in some cases where talking about people, the idea of spirit is that of wind or of expelled breath. What I mean is, the Spirit is called the word of God (Eph 6:17). When we speak words it is generally through the exhalation of breath. So sometimes when the Bible speaks of the Spirit of God coming on someone it may mean that God's inspired (there's the word again) word came to them.
For the most part, though, I think the first distinction is the best. The spirit is the life in a man, and the soul is the will or consciousness that will live after we draw our last breath (spirit).
I hope this helps. Thanks for the question.