It should be an easy thing to explain, and it is indeed. It's quite simple.
Repentance is simply a change of mind, however, it isn't just that alone. While this is what repentance entails, a change of life assumes, a change of life.
So what does it involve?
This is recognizing that you have done something wrong, this is the first step. You recognize that you have sinned against a holy God, that you have violated his law and you see how wicked you really are in his sight. Accept his offer of atonement and you will be cleansed
The next step is to get rid of the things that God doesn't like, namely idols and sin. There are numerous exhortations in the New Testament to live holy lives which I can list here:
"John 8:11"No one, sir," she said. "Then neither do I condemn you,"Jesus declared. "Go now and leave your life of sin.""
"Romans 6:1 What shall we say, then? Shall we go on sinning so that grace may increase? 2 By no means! We are those who have died to sin; how can we live in it any longer? 3 Or don’t you know that all of us who were baptized into Christ Jesus were baptized into his death? 4 We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life."
"1 Corinthians 6:9 Or do you not know that wrongdoers will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor men who have sex with men[a] 10 nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God. 11 And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God."
"1 Peter 4:1 Therefore, since Christ suffered in his body, arm yourselves also with the same attitude, because whoever suffers in the body is done with sin. 2 As a result, they do not live the rest of their earthly lives for evil human desires, but rather for the will of God. 3 For you have spent enough time in the past doing what pagans choose to do—living in debauchery, lust, drunkenness, orgies, carousing and detestable idolatry. 4 They are surprised that you do not join them in their reckless, wild living, and they heap abuse on you. 5 But they will have to give account to him who is ready to judge the living and the dead. 6 For this is the reason the gospel was preached even to those who are now dead, so that they might be judged according to human standards in regard to the body, but live according to God in regard to the spirit."
"James 1:19 My dear brothers and sisters, take note of this: Everyone should be quick to listen, slow to speak and slow to become angry, 20 because human anger does not produce the righteousness that God desires. 21 Therefore, get rid of all moral filth and the evil that is so prevalent and humbly accept the word planted in you, which can save you."
Let me make this clear, We will NOT be automatically perfect, we will make mistakes, the Christian journey is a road, it's an ongoing journey. There is a difference between falling into sin and practicing sin. Though Christians stumble into the former, they, if truly regenerate will not persist in sin. It's one thing to be a nominal and never believe to begin with, but it's quite another to start and never finish.
If there is anyone you have hurt or offended, you definitely need to put it right if you can. Jesus himself highlights this point in the Sermon on the Mount when you have offended a brother in Christ:
"Matthew 5:23 “Therefore, if you are offering your gift at the altar and there remember that your brother or sister has something against you, 24 leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift.
25 “Settle matters quickly with your adversary who is taking you to court. Do it while you are still together on the way, or your adversary may hand you over to the judge, and the judge may hand you over to the officer, and you may be thrown into prison. 26 Truly I tell you, you will not get out until you have paid the last penny."
While Jesus is referring to what you should do if you have offended someone in Christ, there is a principle here that applies when you have been drawn to God and come to him. Is there someone be they unbeliever or believer that you have lied to, maybe you stole from them or have caused damage to them, including mental damage? If so, try to put the past right if you can. If you are not able to patch things up, pray for forgiveness and ensure such an incident doesn't happen. If someone turns down your forgiveness, you have done what you can and there isn't much you can do, but solace in the fact that God has forgiven you. *Sometimes it may involve dealing with criminal activity you have committed, confessing to the crime and being prepared to face punishment.
The Old Testament has principles of restitution and many examples could be cited as found in Exodus 22 which can be read here: https://www.biblegateway.com/passage/?search=Exodus+22
Making amends isn't something that should be disparaged, It is something that should be seen as not only a noble thing, but also biblical. The Proverbs strike this point home:
"Proverbs 14:9 Fools mock at making amends for sin,
but goodwill is found among the upright."
Sometimes we all feel we have done something we feel is so bad, that we cannot be forgiven, That is simply NOT the case. Don't assume that you are beyond redemption when you have done wrong, no matter how small or large sin is. God is there ready to forgive your transgression, even a big serious one that could cost you friends or family. No sin is unforgivable, except Blasphemy of the Holy Spirit. Every sin before God aside from that can be completely covered and washed away. You may not be able to forget, but God will, since in the new covenant he says "I'll remember their sins no more", As found in Jeremiah 31:31. Once you have turned to him and repented, there is no need to dwell on the past and you have learned a new lesson and can move forward.
I hope this article has been of help to you and I thank you for taking the time to read.
*Added on the 15th of October 2017