Barclay's commentary on Acts 2.38

Acts 2:36-38 (ESV) 
36 Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified.”
37 Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?”
38 And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.

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From Barclay's Daily Study Bible,

"This passage shows with crystal clarity the effect of the Cross. When men realised just what they had done in crucifying Jesus their hearts were broken. "I," said Jesus, "when I am lifted up from the earth will draw all men to myself" (Jn 12:32).  Every man has had a hand in that crime. Once a missionary told the story of Jesus in an Indian village. Afterwards he showed the life of Christ in lantern slides thrown against the white-washed wall of a house. When the Cross appeared on the wall, one man rose from the audience and ran forward. 'Come down from that Cross, Son of God,' he cried. 'I, not you, should be hanging there.' The Cross, when we understand what happened there, must pierce the heart.

That experience demands a reaction from men. "Repent," said Peter, "first and foremost." What does repentance mean? The word originally meant an afterthought. Often a second thought shows that the first thought was wrong; and so the word came to mean a Change of mind. But, if a man is honest, a change of mind demands a change of action. Repentance must involve both change of mind and change of action. A man may change his mind and come to see that his actions were wrong but be so much in love with his old ways that he will not change them. A man may change his ways but his mind remains the same, changing only because of fear or prudence. True repentance involves a change of mind and a change of action."