Even before the New Testament there were baptisms. The high priest needed to bathe in water twice on the day of Atonement. Lev 16:4,24 When someone was ceremonially unclean, they often were required to bathe to become ceremonially clean again. So washing with water was some thing normal to the Jew. Also Gentile proselytes went though a baptism of sorts when they wanted to join the people of God. This washing was to remove their "gentileness". It made them clean, because as Gentiles they were ceremonially unclean. Then John the baptist appeared on the scene baptizing people, that is he plunged, dipped, or immersed them in water for that is what to baptize means. His baptism was a baptism of repentance. When people came to John to be baptized, they were admitting that they were unclean from their sins and needed to be washed clean. This was to prepare them for the arrival of the Messiah who would wash the truly repentant from their sins by His blood. But Christian baptism means something more than John's baptism.
First, let it be noted that the Head of the Church, Jesus Christ, commands believers to be baptized. "All authority in heaven and on earth has been given to me. Go, therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you." Matt 28: 18b-20a We are to preach the gospel to all peoples. Those that repent are to be baptized and then they are to be taught what our Lord taught His disciples. That is pretty simple isn't it. It is significant that it doesn't read baptizing them and their children. If He did that would settle the issue wouldn't it? Some have argued this passage deals with a missionary context. Well even in a missionary context, some new believers will have children. Do you not think that of the 3000 new converts that were baptized on Pentecost, none of them had families and children? Yet we only read that the 3000 converts were baptized. Baptism is not an option, it is a command given by Christ. Let us look at what baptism signifies.
1) Baptism pictures the washing of our sins away by Jesus.
The act of baptism doesn't do any thing apart from faith. The water is not holy or magical. Baptism, like Lord's supper, doesn't do good to the one without faith. This is shown in 1 Peter 3:21. After explaining how the ark saved Noah and his family from the flood Peter says, " Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a good conscience, through the resurrection of Jesus Christ." The ESV study note says this on verse 21, " meaning that the passing of water over the body does not cleanse anyone. Baptism saves you because it represents inward faith, as evidenced by one's appeal to God for the forgiveness of sins." Baptism is an outward picture that represents an inward reality. We use water to clean our bodies from dirt and grime. So the death and sacrifice of Jesus Christ when applied to a repentant sinner washes away our sins and we are now clean in God's sight. We can see this aspect of baptism in Titus 3:5 where the regeneration is called "the washing of regeneration and renewal of the Holy Spirit." This washing of regeneration is what baptism pictures. Or Acts 22:16, Ananias said to Paul, " Get up and be baptized, and wash away your sins calling on His name." Again baptism here pictures the washing away of sins. Through out the New Testament there is a close connection between the inward work of regeneration and the outward picture of baptism.
2) Baptism pictures the dying of the old man and the coming to life of the new man.
"Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him though baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life." Rom 6:3-4
Consider Col 2:12 " having been buried with Him in baptism, in which you were also raised up with Him though faith in the working of God, who raised Him from the dead."
Baptism pictures our identification and unity with Christ. "For as many of you as were baptized into Christ have put on Christ." Gal 3:27 His death was the death of our old natures. His resurrected life from the dead was our new life in the inner man. We died with Him and we were raised to new life with His resurrection. This is what happens when we are born again. Baptism pictures this union with Christ.When we go down into the water as if we were drowning, it pictures our death of the old man in Christ. When we come up from the waters, it pictures our new life in Christ as we again can breath the air. It is because of this symbolism in baptism, that immersion or dunking is the best mode for baptism. Only this mode of baptism fully pictures all that baptism was intended to picture. Baptism points back to one's conversion while circumcision points forward to one's need for conversion. This is the connection between baptism and circumcision. See Col 2:11-13
3) Baptism is also a public profession of faith and one's commitment to follow Christ.
While no texts bring this aspect out, it is an implication. Being baptized is showing to others that God has saved me and made me united to Christ so now I am a new creature and will live for the Lord Jesus rather than myself. In some countries or cultures when a new convert is baptized it is a serious statement to others that I am leaving my old life and I am a new person. This often results in great persecution. With those who practice infant baptism, they separate this aspect from baptism. They have a profession of faith ceremony years later when the child professes faith in Christ. This ceremony was not done in Old Testament Israel after circumcision. Nowhere in the New Testament do we find any basis for this later public profession of faith. It is not necessarily wrong, but God's ideal laid out in His word, is that baptism and profession of faith go hand and hand.
While this is only a brief look at what baptism means, it should be clear that it fits perfectly with what God promises to do to those in the new covenant. Baptism's meaning also rules out applying this ordinance to infants. Baptism is designed to strengthen new believers with giving them a beautiful picture of the inward work of God in their lives.