A few things are going on here. First, Jesus just told the eleven that all authority had been granted to Him. Because He possessed that authority He commanded the eleven to make disciples of the all the nations, "baptizing them in the name of the Father and the Son and the Holy Spirit." Why? Some thoughts...
1. Radical and substantive change in the relationship Judaism had with Yahweh. Instead of the Father being the pivotal person of worship under the Old Covenant, the Son and the Holy Spirit are now revealed as equal.
2. Are disciples baptized “in the name of”, as in identification; or are they baptized “into”, denoting entrance into a group, association or community? I believe it is both. They are certainly identified with the Holy Trinity, the substantive change over the Old Covenant. This is the symbolic power of baptism that Paul writes about.
1 Peter 3:21 Corresponding to that, baptism now saves you-- not the removal of dirt from the flesh, but an appeal to God for a good conscience-- through the resurrection of Jesus Christ. This places less emphasis on element and mode and more on the substance of the new birth. But there is no doubting that baptism is also a pronouncement to the family of God that someone is professing their faith. It is not a public pronouncement to the world since they have no part in Christ. It is very much a covenant identification to and with the people of God, by the authority of Son (Matt. 28:18), and identification with the Holy Trinity (Matt. 28:19).
