A really good question.
1. The answer lies partly in the core meaning of “repentance”.
Contrary to popular but incorrect teaching, “repent” does not mean “180-degree turnaround” or “putting away sin” or any other ACTION.
It simply means “change your mind”. This comes from both the literal Greek word metanoia (meta…, “change”, and …noia, “mind”), as well as biblical context.
True, when we change our MIND it logically will result in changing our ACTIONS as well, but the repentance is in the mind and prior to the action.
2. Although “repentance” is usually used in regard to one’s sins, it actually applies to any change from a false belief to a true one.
For example, one can “repent” from unitarianism to trinitarianism, or from legalism to grace. (So ironically, in regards to our original question, we can see that “legalism” itself is something to be “repented of”, that is, to change one’s mind about.)
3. As far as “repenting of one’s sins”, contrary to popular but incorrect teaching, “repentance” is not “turning from one’s sins”, as most gospel tracts admonish. It’s actually “changing one’s mind” about their sins.
In what way?
Well, the sinner is not really *against* his sins. He either defends them as “not that bad”, or even goes so far as to glory in them, as in, “I’m evil, I know I’m evil, and I intend to stay evil, and I want to go to Hell because that’s where my friends will all be.”
When one “changes his mind” about his sins, he comes to see the truth that his sins are not only bad and wrong, but are sins against the Holy God Who created him. He now is *against* his sins, and coincidentally has “changed his mind” about Jesus Christ in Whom he now believes, as Lord and Savior and Forgiver of his sins.
This profound “change of mind” will certainly result in a profound “change of actions” (contrary to the Ryrie/Hodges folks who teach that one can “believe” with no change in their lives), but such change in actions may be drastic, somewhat gradual, or up and down like an EKG chart — depending on how well the newer believer is taught to walk by the Spirit.
4. All repentance is ultimately a gift from God, “granted” by God initially through being born again, aka “regeneration” or “a new heart”.
Although preaching, “Repent!” (“Change your mind!”) is certainly legitimate, the idea that one can change their own mind as an act of their will apart from the Holy Spirit is unbiblical. Thus our preaching/witnessing should always be accompanied by prayer.
5. All repentance is in regards to TRUTH. Biblical repentance is nothing more than “changing our mind” about what is true.
Examples for born-again believers:
If we think God “condemns” believers on the basis of their newest sins, we need to repent and believe the Scripture which says there is no condemnation to those who are in Christ Jesus, and that all our sins have already been forgiven.
If we think we are “just like the lost person except we’re saved”, we need to repent and recognize that we have been given a new heart, a new spirit that hates sin and loves righteousness because we love Jesus.
If we think that God loves and favors us on the basis of our performance (that we are “under law”), we need to repent and believe that God loves and favors us because He chose to, sovereignly, and on the basis of the death, burial and resurrection of our Lord Jesus Christ (we are “under grace”, Rom. 6:14).
If we believe that He might leave us and forsake us if we ACT bad enough, we need to repent and believe that He will never leave us nor forsake us, having bought us by the blood of Jesus.
6. Finally, believers are often temporarily deceived by the world, the flesh and the devil. When this happens, we sin, blinded for a moment (or hour or day, etc.) to the truth we have already learned about our sins.
When this happens, we are called upon to once again “repent”, “change our mind”, about such sins, and return to the truth and to walking by the Spirit.
We thus should be “quick repenters”, not running FROM the Lord to hide our foolish sins, but running TO Him, confessing our sins and thanking Him for His already-done forgiveness.
Thankfully, if we remain in our deceived state, and continue in these sins, the Lord will lovingly chastise us, with the purpose of bringing us back into the truth and in communion with Him.
His chastisement is never punitive, that is, it is not designed as tit-for-tat punishment, but is loving correction, no matter how “rough”, and is part of working all things together for our good.