Albert Barnes Commentary Acts 19:4

"And Paul said, John baptized with the baptism of repentance, saying unto the people that they should believe on him that should come after him, that is, on Jesus." — Acts 19:4 (ASV)

John verily baptized. John did indeed baptize.

With the baptism of repentance. This baptism had a special relation to repentance, or was a profession that they repented of their sins (see Barnes on Matthew 3:6).

Saying unto the people. The design of his coming was to turn the people from their sins and to prepare them for the coming of the Messiah. He therefore directed their attention principally to him that was to come (John 1:15, 22-27).

That is, on Christ Jesus. These are the words of Paul, explaining what John taught. He taught them to believe in the Messiah, and that the Messiah was Jesus of Nazareth. Paul's argument is that it was highly proper for them now to publicly profess that Saviour to whom John had borne such explicit testimony: "Jesus is the Messiah for whom John came to prepare the way; and as you have embraced John's doctrine, you ought now publicly to acknowledge that Redeemer by baptism in his name."