The gospel cuts to the heart. Peter's message of Jesus crucified brings conviction that demands a response. The people cry out, "What shall we do?"--the same question every honest heart must ask when confronted with truth.
Verse 38 gives God's answer. Repentance turns us from sin, baptism in Jesus' name washes those sins away, and the gift of the Holy Ghost fills us with God's Spirit. This is not optional or symbolic--it is the pattern of salvation given by the apostles themselves.
The promise is generational. Peter declares it is for "you, your children, and all that are afar off." That means this new birth experience stretches across time and culture. What was poured out on Pentecost is still available today.
The result is transformation. Three thousand souls were added in one day because they obeyed the Word. The same obedience brings the same results now--repentance, baptism in Jesus' name, and the infilling of the Holy Ghost remain the foundation of the Apostolic church.