According to the English Dictionary It's defined as a process of compensation for losses. Also said to be the act of making good or compensating for loss or injury.
Restitution is an age long Christian principle and practice which unfortunately in this age and time is being downplayed on. But it ever remains important. It is true that when a person comes to know Christ, his it her sins are forgiven, being washed with the blood of Jesus which was shed on the cross of Calvary, an ultimate payment for all our wrongs, but as long as you did not get translated into heaven the moment you got saved, there are certain wrongs high you did to follow men for which you must make amends as an evidence of your new found faith, and as a proof of your love for God reflecting in your love for man. Because the Bible says "how can you say you love God whom you cannot see when you do not love your fellow man whom you see"?
Some of the ways restitution Is made 
- Rendering Apology :
There are people you wronged and hurt so bad and you just ignored them because you were not saved and so it really didn't care then, but now you are saved and you remember your wrong, you have to admit your wrongs to those people and plead for forgiveness.
- Restoration:
If you stole something from someone, and you are still in possession of it, you cannot be said to be a child of God as long as you are making use of a stolen property. There is a difference between falling into sin and livin in sin the later being a deliberate act which is proof of an unregenerate heart. You have to return the stolen good to the owner even with some interest according to the Bible, except in a case where you can no longer locate the Person.
- confession
There are offences the you committed for which nobody knew you are the one, and there has been a great confusion as to how that offence was committed as well as who did it, possible an innocent person might have been accused and punished for your offence. Now you are saved, your salvation cannot be genuine if you leave that innocent person languishing in prison or moving around with a stigma for something you did, you have to make it right by confessing.
These are just a few ways and areas one needs to make amends. I hope you find them helpful as you decide to live a descent Christian life
note you need wisdom from God and wise counsel from God's servants who a genuine on how to go about it
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Also checkout my last post how to change your life for good.
Thank you for reading. I remain your favourite life couch @drchuka