Walking in this "newness of life," is an exercise in, it is a practicing of walking in, eternal life. Only God has eternal life inherent within Himself. Only God has eternal life to give. As the Father has life inherent within Himself, He has given this life to His Son, the Christ, to have immortal life inherent within Him. Then through Christ, God gives it to us. Whoever does not have Christ does not have eternal life. Eternal life is a gift that no human has, until he receives it as God's gift.
This is the amazing symbolism—the true meaning of baptism. It pictures, in symbol, the death, burial, and resurrection of Christ.
This symbolism is a dual picture, as all things in God's plan are dual in operation. It pictures the crucifixion of the old self, or of the sinning life, the burial of this sinning self, and the coming up out of this watery grave, symbolic of a changed person resurrected to a new, righteous, spiritual life in Christ Jesus.
Baptism also symbolizes purification which prepares a person for the receipt of the Holy Spirit.
These 5 verses are packed full of symbolism. Baptism pictures:
Going down into the water—burial in the water pictures the death of Christ, and of the old self. Coming up out of the water pictures Christ's resurrection, and a spiritually resurrected person walking from that day on "in newness of life."
Water baptism is the ordinance ordained of Christ by which we express our faith in Christ as Savior—our acceptance of His death, burial, and resurrection for us, and our repentance of the old life and burial of it, rising to new and higher life from that day on. It is a wonderful ordinance, full of meaning.
We are "baptized into Jesus Christ." Reading verse 3 again, "...do you not know that as many of us as were baptized into Christ Jesus were baptized into His death?"
Not into some church organization or denomination. We are to be baptized into the divine family —the family of God. And it is to be done "in the name"—by the authority—of Jesus Christ.