There, in chapter 2, it was said: "that He might redeem us from all iniquity and purify for Himself a chosen people." It remained unclear how redemption and purification are accomplished in each of us. Here, in chapter 3, it is explained that this is accomplished in Baptism: "He saved us by the washing of regeneration and renewal."
Christ redeems and purifies not only by teaching. He does this not only by outwardly imputing to us His righteousness and purity, but also by giving us new life and renewing our whole being.
This rebirth into new life is accomplished by a washing, by which one can understand only a washing with water (Eph 5:26), a sanctifying and justifying washing (1 Cor 6:11), in a word, Baptism.
In this water Baptism, regeneration and renewal are accomplished by the power of the Holy Spirit. For Him, the act of immersion and sensible water serve only as means and instruments.
Therefore it is said: "of regeneration and renewal by the Holy Spirit, whom He," God the Father, "poured out upon us," in Baptism, "through Jesus Christ."
Here the participation of all Three Persons of the Godhead in our regeneration and renewal is indicated. To this corresponds the celebration of Baptism in the name of the Father, and of the Son, and of the Holy Spirit.