You have to go back and read what Peter was telling these people in the previous verses. We are saved by grace through faith. Faith only comes by hearing the Word of God. These people were listening to the Gospel through the Word of God spoken through Peter. To repent is to change your mind, and in this case who Jesus Christ was. Jesus is the Son of God, making him equal to God. This revelation is what causes a man to get saved as it is written in Roman 10:9
Rom 10:9.. That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Rom 10:10.. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
See these verses here in Romans 10:9-10. This is what I did almost 40 years ago, and I have never been the same!
Act 2:32.. This Jesus hath God raised up, whereof we all are witnesses.
Act 2:33.. Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.
Act 2:34.. For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
Act 2:35.. Until I make thy foes thy footstool.
Act 2:36.. Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.
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?
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.