The first point is Peter's exhortation for those in the crowd to repent. Repentance , is often misunderstood, and means much more than simply being sorry for past actions. Repentance includes sorrow for sin, but it is not merely the emotional response we feel when we are caught in the act of sin. Those who therefore turn from their former way of thinking, and who come to realize that confidence in themselves and their own righteousness is futile, and who also come to realize that Jesus Christ is the only savior from sin, have repented , and are promised the forgiveness of sin. The second thing to consider here is baptism.
Baptism is commanded as the outward sign of the inward act of repentance.
To those in the crowd that day, Peter's exhortation certainly harkened them back to the words of John the Baptist. For John had also linked his baptism of repentance to the forgiveness of sin. And here in his Pentecost sermon, Peter does not flinch from linking the outer sign of baptism directly to the inward act of repentance. There are several important things to keep in mind here. First, the rite of baptism itself does not forgive sin.