Human beings do have a spiritual component to our makeup. As Job 32:8 says, "There is a spirit in man." And the apostle Paul pointed out, "For what man knows the things of a man except the spirit of the man which is in him" (1 Corinthians 2:11).
It is this human spirit that imparts human intellect to our physical brains, creating the human mind. It is what makes people vastly more intelligent than animals.
Yet this spiritual aspect of human existence is nothing like the immortal soul concept. The spirit in man is not animate of itself. It is not a spirit entity that "lives on" after death. As Scripture shows, the human spirit has no consciousness apart from the body, for man is mortal. When we die, we will have no awareness of anything at all—until, that is, the future time when God places our individual spirits within new bodies He will give us, thereby bringing us back to life.
The human spirit is critical to our destiny, since God's Holy Spirit joining with it is what makes us God's children (Romans 8:16). And just as the human spirit gives us human understanding, so God's Spirit gives us higher, godly understanding (1 Corinthians 2:10-16). We are not born with the Holy Spirit but receive it from God following repentance and baptism (Acts 2:38).