In my opinion our souls are our wills (or identity). What we do and say is who we are. The will to love God or reject God. At the point of conception God in-souls the hardware (our physical identity aka. flesh aka. dust of the earth) as He did with Adam.
Beasts have souls as well, however they do not have a spirit and cannot have communion with God. Prior to the fall, the beasts were subject to Adam. Their souls/ wills were directed by him. After the fall the souls/ wills of the beasts were in subjection to the new ruler of this world (destruction and death). We see a glimpse of how beasts were originally in subjection to Adam when Jesus Christ was in the desert with the wild beasts in subjection to Him.
Mar 1:13 And he was there in the wilderness forty days, tempted of Satan; and was with the wild beasts; and the angels ministered unto him.
Adam was originally created with his spirit ruling his soul, and his flesh in submission to his spirit. He had perfect communion with God. When he fell (intentionally disobeyed), his soul became ruled by his flesh and his spirit became submitted to his flesh (spiritually dead to his flesh). This is why God did not want Adam to eat from the tree of life, because his spirit would be permenantly submitted to his flesh for eternity and his soul could never have spiritual communion with God again.
Satan took over dominion of this world with Adams failure. Our flesh is enslaved to Satan before we become believers.
The virgin birth of Christ circumvented the rulership of the flesh passed down from Adam, and Christ's spirit ruled from day one. Christ's flesh was still subjected to the curruption of this world, yet he never submitted to it. He required a new eternal body as we do. In His new body He was unrecognizable by His disciples (He stills bears the marks of His sacrifice, however).
Our souls are created (because they were created, we never inhabited eternity as God does). Our earthly flesh is not eternal and needs replacment. Because our spirit and soul are eternal, when we become believers we untaintedly enter into the heavenlies.
Eph 2:5-6
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
6 And hath raised [us] up together, and made [us] sit together in heavenly [places] in Christ Jesus:
Jeremiah 1:5 and Romans 9:10-13 describes the soul having a history before being placed in the flesh.