[3:5] [It was] not by works of righteousness which we have done, but according to his mercy he [gave] saved us [salvation], [through] by the washing of regeneration, and renewing of the Holy Ghost.
Not by works of righteousness is a direct reference to the Jewish focus on works of the Mosaic Law. This becomes clear when he ads which we have done—reminiscent of his pharisaic background prior to conversion. No amount of personal pedantic righteousness on our part can produce salvation. Divine intervention and priesthood authority is necessary to make saving ordinances efficacious.
The washing of regeneration (Greek loytroy paliggenesias, λουτρου παλιγγενεσιας) is a term meaning the ordinance of baptism by immersion. This is a beautiful express, and very descriptive. The word washing (loytron λουτρον) means both a bath or a wash basin. The word regeneration (paliggenesia παλιγγενεσια) appears only twice in the New Testament (Matthew 19:28; Titus 3:5). This word literally means a rebirth. Classical writers use this word in reference to the changes produced by the return of spring.
Renewing (Greek anakainosis ανακαινωσις) in this instance refers to a revival or restoration of what previously existed. This conveys the concept of a restoration to the fellowship we once enjoyed. On three other occasions, Paul referred to the gift of the Holy Ghost as “the earnest of our inheritance” back in the kingdom of God. (William Victor Blacoe, Understanding the New Testament: An Interpretive Translation and Exhaustive Commentary of the New Testament Epistles of Paul the Apostle to Timothy, Titus, and Philemon [Springville, UT.: Cedar Fort, Inc., 2011], 145)