Please define and explain the characteristics of the soul and the spirit of man.

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 12:30And thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind, and with all thy strength: this is the first commandment.
See All...; Luke 10:27And he answering said, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy strength, and with all thy mind; and thy neighbour as thyself.
See All...). 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 5:23And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ.
See All..., "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 24:39Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
See All... with 1 Corinthians 15:50Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
See All...).

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 6:9And when he had opened the fifth seal, I saw under the altar the souls of them that were slain for the word of God, and for the testimony which they held:
See All...). 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 [19] There was a certain rich man, which was clothed in purple and fine linen, and fared sumptuously every day: [20] And there was a certain beggar named Lazarus, which was laid at his gate, full of sores, [21] And desiring to be fed with the crumbs which fell from the rich man's table: moreover the dogs came and licked his sores. [22] And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried; [23] And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom. [24] And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame. [25] But Abraham said, Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented. [26] And beside all this, between us and you there is a great gulf fixed: so that they which would pass from hence to you cannot; neither can they pass to us, that would come from thence. [27] Then he said, I pray thee therefore, father, that thou wouldest send him to my father's house: [28] For I have five brethren; that he may testify unto them, lest they also come into this place of torment. [29] Abraham saith unto him, They have Moses and the prophets; let them hear them. [30] And he said, Nay, father Abraham: but if one went unto them from the dead, they will repent. [31] And he said unto him, If they hear not Moses and the prophets, neither will they be persuaded, though one rose from the dead.
See All..., 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 2:1And you hath he quickened, who were dead in trespasses and sins;
See All..., 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 12:7Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
See All... 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 8:16The Spirit itself beareth witness with our spirit, that we are the children of God:
See All...). God's Spirit bears witness with our spirit.

1 Corinthians 2:9-16 [9] But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him. [10] But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God. [11] For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God. [12] Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God. [13] Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual. [14] But the natural 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. [15] But he that is spiritual judgeth all things, yet he himself is judged of no man. [16] For who hath known the mind of the Lord, that he may instruct him? But we have the mind of Christ.
See All... 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 2:12Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.
See All...). 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 2:14But the natural 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.
See All...). 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.