I think it is widely taught that the Jewish people were being told to repent from sins and sinning. Yet reading Peter's words in the context of the passage, it appears he is telling them to repent (change their minds) about Jesus whom they had rejected.
He first informed them that they had killed the messiah:
Acts 2:23 KJV
23. Him, being delivered by the determinate counsel and foreknowledge of God,
ye have taken, and by wicked hands have crucified and slain:
In light of what he said, they replied "what must we do to be saved?"
Act 2:37 Now when they heard this, they were pricked in their heart, and said unto
Peter and to the rest of the apostles, Men and brethren, what shall we do?
In my ear, they are pricked in their heart about their rejection and killing of the Messiah. That is what they meant when they said "what shall we do?"
So when Peter said to repent (change your mind), he was talking about repenting (change their minds) about their rejection and killing of Jesus.
Act 2:38 Then Peter said unto them, Repent, and be baptized every one of you
in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Repent of your rejection of Jesus as your messiah, and (instead) be baptized in His name (as the Messiah) for the remission of sins.
But yes, we need to turn from our sins, but in this particular passage, Peter is talking about repenting from the rejection and killing of Jesus.