First off let's talk about what it is not:
1. Repentance is not doing penance. Many Catholic Bibles translate “repentance” as “do penance.”
2. Repentance is not reformation or changing one’s life.
Repentance isn't changing your life and giving up sin in order to be saved.
3. Repentance is not mere remorse for wrong actions.
2 Corinthians 7:10 KJV
[10] For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death.
A lot of people feel bad for the consequences of sin and they feel bad about how they have lived, this is not repentance.
We see this in the Prodigal Son. He was not merely remorseful of how he had lived and of the consequences he had suffered; he came to the place where he acknowledged first and foremost that he had “sinned against heaven” (Lk. 15:18).
The word repent is one Greek word: metanoio
Two Greek root words here
Meta-change of place or condition
Noio-to exercise the mind, to think, to comprehend
The word repent could be defined as change your mind.
there are three areas people must have a change of mind about:
1. Sin must be acknowledged and confessed
Psalm 51:3 KJV
[3] For I acknowledge my transgressions: and my sin is ever before me.
Psalm 51:4 KJV
[4] Against thee, thee only, have I sinned, and done this evil in thy sight:
2. Self must be realized and admitted to be wicked and that my works mean nothing in the eyes of God:
Rom 3:23, 3:10, Jeremiah 17:9
Hebrews 6:1 KJV
[1] the foundation of repentance from dead works, and of faith toward God,
Repentance is saying "God I am not good and I can't make myself good, I need you to give me a new heart"
Luke 18:9-14 KJV
[9] And he spake this parable unto certain which trusted in themselves that they were righteous, and despised others: [10] Two men went up into the temple to pray; the one a Pharisee, and the other a publican. [11] The Pharisee stood and prayed thus with himself, God, I thank thee, that I am not as other men are , extortioners, unjust, adulterers, or even as this publican. [12] I fast twice in the week, I give tithes of all that I possess. [13] And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner. [14] I tell you, this man went down to his house justified rather than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.
Luke 5:30-32 KJV
[30] But their scribes and Pharisees murmured against his disciples, saying, Why do ye eat and drink with publicans and sinners? [31] And Jesus answering said unto them, They that are whole need not a physician; but they that are sick. [32] I came not to call the righteous, but sinners to repentance.
3. And lastly the Saviour:
John 14:6, ACts 4:12, John 3:16
I believe a great example is the Thief on the cross:
Luke 23:32-33 KJV
[32] And there were also two other, malefactors, led with him to be put to death. [33] And when they were come to the place, which is called Calvary, there they crucified him, and the malefactors, one on the right hand, and the other on the left.
Luke 23:39-43 KJV
[39] And one of the malefactors which were hanged railed on him, saying, If thou be Christ, save thyself and us. [40] But the other answering rebuked him, saying, Dost not thou fear God, seeing thou art in the same condemnation? [41] And we indeed justly; for we receive the due reward of our deeds: but this man hath done nothing amiss. [42] And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. [43] And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.