Commentator Albert Barnes explains:
The word "life" in this passage is used evidently in two senses. The meaning may be expressed thus: He that is anxious to save his "temporal" life, or his comfort and security here, shall lose "eternal" life. . . . He that is willing to risk or lose his comfort and "life" here for my sake, shall find "life" everlasting, or shall be saved.
Jesus attaches a double meaning to the word "life": a lower, physical, and temporal meaning and a higher, spiritual, eternal meaning. Christ warns us that we must make an entire sacrifice of the lower for the higher. For if we do not completely and wholeheartedly surrender the lower for the higher, we will lose both. "When we learn how to die, we learn how to live." Indeed, to learn how to die physically is to learn how to live spiritually (Romans 6:6; II Corinthians 5:17).
Then Jesus said to His disciples, "If anyone desires to come after Me, let him deny himself, and take up his cross, and follow Me. For whoever desires to save his life will lose it, but whoever loses his life for My sake will find it. For what profit is it to a man if he gains the whole world, and loses his own soul? Or what will a man give in exchange for his soul?" (Matthew 16:24-26)
As Christ tells us, if we want to seek Him, we must follow Him and surrender to God everything—our wills, our bodies, and our lives. The self must be denied because our carnal mind is driven by pride and an underlying belief and desire that we must get things for ourselves. We must subsequently live our lives as living sacrifices (Romans 12:1), following Christ's example of complete submission to the Father's will. If we are anxious to save, to preserve, our physical lives and/or to put our security in physical things, we will lose our spiritual lives.
Those who seek to gain the world's physical treasures (Matthew 6:19-21) will lose the Father's spiritual treasures. All of the world's physical treasures are not enough to purchase one eternal life, but if we are willing to sacrifice everything—and it takes everything—if we, with complete trust in Him, put everything in our faithful Creator's hands, we will find everlasting life.
As Christ tells us in Matthew 10:39 and its parallel scriptures, if we want to know Him, we must surrender everything to God. He instructs us to follow His giving example of total self-sacrifice in devotion to God's will. He teaches us to deny the self because our carnal mind is driven by the way of get, which always forces us off the right path. Finally, He advises us to sacrifice entirely the lower, physical, temporal life for the higher, spiritual, eternal life. For if we do not completely and wholeheartedly surrender the lower for the higher, we will lose both.
In our daily prayer and self-evaluation, we should ask ourselves, "Is today the day? Have I surrendered everything to God and am I ready? Am I doing all I need to do? Am I being the person that God wants me to be?" We must remember that life can end in an instant, but we are to live in the fear of God, not in the fear of death. In order to live, we must first learn to die.