“Regeneration” has two distinct and different meanings. 1) The way the Bible uses the term. 2) The way theologians use the term.
2. Theologians talk about “regeneration” as an equivalent to the term “born again” and by that they usually mean an ontological change in the soul of a man as he is changed from being dead in trespasses and sins, to being alive by the Spirit in Christ. This is what happens when you come to faith and Get Saved. You used to be Dead spiritually. Now you are Alive: born of the Spirit. That is generally what theologians are talking about when they talk about “regeneration.”
1. But the Bible doesn’t use the term that way at all. In fact the word regeneration, (palin-genesia, again-generation) occurs only twice in scripture:
Matthew 19:28 Jesus said to them, “Truly, I say to you, in the new world [!!regeneration!!], when the Son of Man will sit on his glorious throne, you who have followed me will also sit on twelve thrones, judging the twelve tribes of Israel. (Matt. 19:28 ESV)
Titus 3:5 he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, (Tit. 3:5 ESV)
You can see how the ESV translators in Matthew recognized their problem. The Greek word is clearly “regeneration”, and it is translated that way in all traditional English translations, but the ESV guys knew that the English word has come to mean something that doesn’t fit what Jesus is talking about. What to do, what to do? Ah! Change Jesus’ word! There.
Or, we could actually submit ourselves to the Bible and retrain our thinking. We could use the word “regeneration” and learn that in the Bible, it is talking about the new age, the new world that comes after the end, in the resurrection. In the regeneration, the Son of Man is sitting on his glorious throne. THEN is the regeneration. Not when you Get Saved.
So when Paul refers to baptism as the washing (loutrou) of regeneration, he is not saying that baptism effects some kind of ontological change in the soul. He is saying that baptism marks you, prepares you, for the age to come. Those who are baptized are marked for life in the regeneration, when the dead are raised, a new genesis, and Jesus sits on his glorious throne.