Scholars still argue over the dichotomy (two-partedness) or trichotomy (three-partedness) of man. I have not heard any arguments for the four- art nature of man even though we are to love the Lord with all our heart, soul, mind, and strength (Mark 12:30; Luke 10:27). Certainly, the aspects of man's nature can be looked in various ways. However, if we have to choose, I fall solidly into the three-fold nature of man camp. Man is made up of body, soul, and spirit. Or, as stated in 1 Thessalonians 5:23, "spirit and soul and body." We will quickly look at all three.
Of course, we know what the body is. It is the material part of our being. The Bible distinguishes the three parts of our body as being flesh (the physical part), bones, and blood (compare Luke 24:39 with 1 Corinthians 15:50).
The soul is the immaterial part of man as we think of a person. It is the person without the body. In the book of Revelation, John "saw under the altar the souls of them that were slain for the word of God" (Revelation 6:9). These souls that were beheaded "cried out with a loud voice" (v.10). Evidently, their souls continued to have voices and mouths even though the physical head had been severed. It seems then that the soul takes the shape of a body.
In Luke 16:19-31, Jesus tells the story of the rich man and Lazarus. They both die. The rich man is buried. Therefore, Lazarus in Abraham's bosom and the rich man in hell are not in their bodies. We are reading descriptions of their souls. Yet, the rich man has eyes (v.23) and he asks that Lazarus dip his finger in water to cool his tongue (v.24). Eyes, fingers, and tongues point to a bodily shape even though their bodies are not there. This is certainly the state of the soul.
Although I know of no individual verse to establish this, the soul seems to be made up of at least three major parts: the mind, the emotions, and the will. That is, our soul is what we think, what we feel, and what we decide. This is why so many passages refer to people simply as souls. The soul is the real person without the body.
What then is left for the spirit? It appears that the entire person is made up of the body and soul. Yet, we must remember. The spirit of a lost man is dead. We are saved when our spirits are quickened, or made alive (Ephesians 2:1, 5). But a lost man appears to be a complete person. So, the role of the spirit in man is spiritual. A man can live his entire life without it. But he cannot know God.
The spirit is the part of man that can know God because the spirit of man is directly of God. Ecclesiastes 12:7 says that "the spirit shall return unto God who gave it." As such, it our spirit that is made alive when we are saved and is directly led by God's Spirit. "The Spirit itself beareth witness with our spirit, that we are the children of God" (Romans 8:16). God's Spirit bears witness with our spirit.
1 Corinthians 2:9-16 is a key passage in understanding the working of God's Spirit though our spirit. We have received "the spirit which is of God; that we might know the things that are freely given to us of God" (1 Corinthians 2:12). The natural man (the lost man) "receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned" (1 Corinthians 2:14). The things of God's Spirit are spiritually discerned. That is, they can only be understood by a spirit that has been brought to life by the quickening of God's Spirit through regeneration. Our spirit is our direct connection with God. God leads us and teaches us through the spirit.
Of course, the Bible says much more about body, soul, and spirit. However, this should give you a starting place.