Here is the first time nephesh is found in the Bible:
Then G-d said, "Let the waters teem with swarms of living creatures, and let birds fly above the earth in the open expanse of the heavens." (Genesis 1:20)
Nephesh is first translated as "soul" several chapters later:
Isaac said, "Behold now, I am old and I do not know the day of my death. Now then, please take your gear, your quiver and your bow, and go out to the field and hunt game for me; and prepare a savory dish for me such as I love, and bring it to me that I may eat, so that my soul may bless you before I die." (Genesis 27:2-4)
In some Hebrew texts the nephesh has been called the "engine of life". Animals also have nephesh souls (see Genesis 1:20 above). The difference between a dead animal and a live animal is usually very obvious (possums not withstanding). The "engine" is not "running" in something that is dead. The nephesh is also sometimes called the "lower soul". It is the part of humanity that drives us towards self-preservation and self-enhancement as regards to our physical drives and desires. In human beings this is much like an "animal instinct" or "natural instinct". As such this "lower soul" in humans is also sometimes referred to as the "animal soul". For all of you New Testament Greek scholars out there, the equivalent word in Greek is psuche.
I mention all this about the nephesh in order to distinguish it from the neshamah.
In Genesis 2:7, we find that G-d breathed the breath of life ( נִשְׁמַת חַיִּים, nishemat chayyom in Hebrew) into Adam’s body that he became a living being ( לְנֶפֶשׁ חַיָּה, l’nephesh chayah). In the Hebraic way of thinking, the neshamah is viewed as the "higher soul" (versus the nephesh/"lower soul"). Animals, too, have a neshamah:
All flesh that moved on the earth perished, birds and cattle and beasts and every swarming thing that swarms upon the earth, and all mankind; of all that was on the dry land, all in whose nostrils was the breath [neshamah] of the spirit [ruach] of life, died. (Genesis 7:21-22)
Sometimes we see a "nobler" side in mammals than we do in fish, birds, and reptiles. Dogs, horses, dolphins, and other animals at times exhibit behavior that is above their animal nature.
Humans, too, can act in a manner above our base, sinful state via this "higher soul" because it is pure and created by G-d and allows us to connect with Him. The morning prayers of Jews from ancient times (including the disciples and likely Christ, Himself) include this:
My G-d, the soul [neshamah] which you have placed within me is pure. You have created it, you have formed it, and you have breathed it into me. You preserve it within me and one day you will take it from me and restore it to me in the awaited future.
Imagine the umbilical cord that connects a mother’s womb to her unborn child. It is the channel through which life flows from the life-giver to the child. In a similar fashion the neshamah connects us with G-d. Life flows from the Life-Giver to the child of G-d. But in our sinful state, that link has been severed and the connection no longer exists. Yes, we still have life via our nephesh but our neshamah is broken. It is only if we are "born again" or "born of the Spirit" (as Messiah says in John 3) that our neshamah is restored in Christ that we "may have life, and have it abundantly" (John 10:10).
So let’s recap: the life G-d created in Adam included a direct connection with G-d (neshamah) between Adam’s flesh and G-d’s Spirit but that connection was broken as a result of sin. Humanity cannot fix this broken connection on our own so Christ paid the price for our sin and the Holy Spirit restores that connection. "For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord." (Romans 6:22) – We have a restored and eternal connection with G-d… in Christ Jesus.
"For while I was passing through and examining the objects of your worship, I also found an altar with this inscription, 'TO AN UNKNOWN GOD.' Therefore what you worship in ignorance, this I proclaim to you. The G-d who made the world and all things in it, since He is Lord of heaven and earth, does not dwell in temples made with hands; nor is He served by human hands, as though He needed anything, since He Himself gives to all people life and breath and all things; and He made from one man every nation of mankind to live on all the face of the earth, having determined their appointed times and the boundaries of their habitation, that they would seek G-d, if perhaps they might grope for Him and find Him, though He is not far from each one of us; for in Him we live and move and exist, as even some of your own poets have said, 'For we also are His children.' (Acts 17:23-28)
May we all live and move and exist in a way that acknowledges our connection to the King and honors Him, the Holy One, blessed be He.