My concise definition of Soul is, EVERY part of a person that is not their body. This in my opinion is completely true and accurate to the word of Our God.
Soul and spirit are intrinsically combined. consider the example from the word, where the sword of the spirit is sharper than any two edged sword, capable of separating bone from marrow and spirit from soul. Think about bone and marrow. Just as the spirit is within the soul, the marrow is also within the bone. The point of that verse was to express the precision of the word, which is truth, and it is a very infinitely precise thing. But it also clearly shows, two things very hard to separate because one is contained within the other in both cases.
We know God as Father Son and Spirit. Literally SOUL BODY SPIRIT. As God's creation this is but one way we are created in his image. If you think of three circles, Our body is the outer shell, within our body is our soul, within our soul is our spirit. We all understand what our body is. Its the physical part of us, that is obvious. Our soul is everything else. It is our personality, it is who we are, what we think what we do, what we love what we hate, it is every choice we make and every decision. Our spirit, is actually everything that animates our body. It is described in the word as, blood, breath, heart beat, and also emotion. If you think of spirit as a path, or river, it is the flow of energy that our soul uses to interact with the world outside itself. Currently our spirit animates our bodies, and we use it every day we live, we use it to create and destroy and communicate, just as God does except God doesnt actually destroy, only corruption does that so, thats us and evil that do that part.
Now, considering what a soul is, it doesnt really matter if a person believes in God or not to understand, Soul is every part of us that is not physical and our spirit is within it. It is not spirit, it is not emotion, it is the essence of who we are. I can explain very clearly why emotion is spirit and show that from scripture, however this isnt within the scope of the op's questions.
All this being said, I really dont see much point in using soul or such discussions to try to show evidence to a non believer. The most powerful evidence is in God's word. Remember the parable of Lazarus? Its in a couple of the gospels. Luke chp 16 i think, the end of the chapter, The last verse of this parable is what brought me to God. It made me search and test and come to understand, the Bible has fulfilled prophecy that are accurate and can actually be proven in a court of law today. The verse is as follows: “He said to him, ‘If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead.’”
Scripture is the only written provable fulfilled prophetic book in this world. There are prophecies written of Jesus from nearly a thousand years prior to his birth, and with accuracy down to the day. This is simply not possible by any means we can prove, yet here is the evidence of it in scripture. We can prove when the books were written. We can prove the historical accuracy of the text. No power we know of besides the God that scripture describes can have such knowledge of events precisely and accurately before they happened. It is indeed more powerful than words spoken from a man who died and came back. Which by the way guys, if you had a friend who died, or family member, and they came back...imagine that. How freaky would that be. How powerful would those words be to you? What Jesus said is true, if they havent believed Moses and the prophets neither will they believe a man raised from the dead. When I deal with people who do not believe, first I get them to agree with me on things they do believe. I believe in and worship, TRUTH, LOVE, HUMILITY, LIFE and SPIRIT, because all of these IS GOD. IF you know the word you know in scripture you can find, God is truth, God is Love, God is humble, God is LIVE, God is SPirit, I can quote each of those verses if you need but you should each find them for yourselves.
May God's abundance of peace and love and joy be with each of you as you walk the path God has set before you doing HIs will in this world.