It has accurately been established that the word "repent" literally means to change one's mind or one's thinking. What the definition cannot mean solely is to "turn from sin". It is absolutely important to change our minds about sinning but remember that even God Himself "repented" and He is not capable of sin (Genesis 6:6-7, Exodus 32:12-14, Judges 2:18, 1 Samuel 15:11, 1 Samuel 15:35, 2 Samuel 24:16, Psalm 106:45, Psalm 135:14, Amos 7:3-6, Jonah 3:10).
Israel's error was rejecting Jesus Christ as their Messiah. Peter's message to "ye men of Israel" was to "repent" about who Jesus Christ was, even after Israel had Him crucified. Their promised earthly kingdom of heaven was still at hand if Peter and the eleven could convince Israel of who Christ was, their Messiah. Their post-cross sins would be forgiven at Christ's second coming to earth to establish Israel's kingdom at the "times of refreshing".
Acts 1:6
When they therefore were come together, they asked of him, saying, Lord, wilt thou at this time restore again the kingdom to Israel?
Acts 3:12-21
And when Peter saw it, he answered unto the people, Ye men of Israel, why marvel ye at this? or why look ye so earnestly on us, as though by our own power or holiness we had made this man to walk?
13 The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Son Jesus; whom ye delivered up, and denied him in the presence of Pilate, when he was determined to let him go.
14 But ye denied the Holy One and the Just, and desired a murderer to be granted unto you;
15 And killed the Prince of life, whom God hath raised from the dead; whereof we are witnesses.
16 And his name through faith in his name hath made this man strong, whom ye see and know: yea, the faith which is by him hath given him this perfect soundness in the presence of you all.
17 And now, brethren, I wot that through ignorance ye did it, as did also your rulers.
18 But those things, which God before had shewed by the mouth of all his prophets, that Christ should suffer, he hath so fulfilled.
19 Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord.
20 And he shall send Jesus Christ, which before was preached unto you:
21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
Christ ascended in glory made manifest to Paul (Romans 16:26, Ephesians 3:9, Galatians 1:11-12) what the mysteries of Christ's death (His shed blood for the forgiveness of sin), burial, and resurrection mean for the world today. Everyone living, since Christ's ascension, has been offered the free unmerited gift of salvation by God's grace through having faith in Christ and what He completed for us on the cross, and without having to first wait for Israel to receive their promised earthly kingdom of priests to the world.
Romans 11:11
I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy.
The basic repentance that Paul speaks of for us all is to realize that we are sinners by nature and in need of God's help to free us from the carnal entrapment of sin that we dwell in and come to the knowledge of the truth in Christ.
1 Timothy 2:3-7
For this is good and acceptable in the sight of God our Saviour;
4 Who will have all men to be saved, and to come unto the knowledge of the truth.
5 For there is one God, and one mediator between God and men, the man Christ Jesus;
6 Who gave himself a ransom for all, to be testified in due time.
7 Whereunto I am ordained a preacher, and an apostle, (I speak the truth in Christ, and lie not;) a teacher of the Gentiles in faith and verity.
2 Timothy 2:24-25
And the servant of the Lord must not strive; but be gentle unto all men, apt to teach, patient,
25 In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth;
What is the truth that we are to acknowledge? What is the foundation that we should all, regardless of denominational origin, should build upon?
Ephesians 1:12-13
That we should be to the praise of his glory, who first trusted in Christ.
13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
Colossians 1:5
For the hope which is laid up for you in heaven, whereof ye heard before in the word of the truth of the gospel;
1 Thessalonians 2:13
For this cause also thank we God without ceasing, because, when ye received the word of God which ye heard of us, ye received it not as the word of men, but as it is in truth, the word of God, which effectually worketh also in you that believe.
Romans 1:5
By whom we have received grace and apostleship, for obedience to the faith among all nations, for his name:
Romans 16:26
But now is made manifest, and by the scriptures of the prophets, according to the commandment of the everlasting God, made known to all nations for the obedience of faith:
Ephesians 2:8-9
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
Hebrews 11:6
But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.
It is first having faith before we are capable of pleasing God. Believing the word of truth, the gospel of our salvation, is where our new spiritual life in Christ begins. It then does not begin by us first "turning from sin".
What then is the relationship between our sins and salvation?
1 Corinthians 15:1-4
Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand;
2 By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
3 For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures;
4 And that he was buried, and that he rose again the third day according to the scriptures:
Romans 5:8
But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
2 Corinthians 5:19
To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
Colossians 1:14
In whom we have redemption through his blood, even the forgiveness of sins:
Romans 3:25
Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
We learn through Paul that the relationship between our sins and salvation is our faith (believing) that God forgave us of all of our sins through Christ's shed blood, burial, and resurrection, and nothing of ourselves. This is when salvation occurs; believing that we were forgiven at the cross. The repentance that post-ascension believers are compelled by Paul to change from is the belief (or faith) that any of our own religious works of self-righteousness will add to what God has already completed on our behalf through Jesus Christ. We are complete in and by Him upon having placed ALL of our faith in Him and His finished work for us:
Colossians 2:6-10
As ye have therefore received Christ Jesus the Lord, so walk ye in him:
7 Rooted and built up in him, and stablished in the faith, as ye have been taught, abounding therein with thanksgiving.
8 Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.
9 For in him dwelleth all the fulness of the Godhead bodily.
10 And ye are complete in him, which is the head of all principality and power:
The righteousness of God is imputed to us upon having placed this faith in Christ. We strive to walk in righteousness from this truth. We do not walk in righteousness to earn our salvation. It is our faith in Christ's righteousness for us that God approves of and how we are made "the righteousness of God in Him".
Romans 4:1-8
What shall we say then that Abraham our father, as pertaining to the flesh, hath found?
2 For if Abraham were justified by works, he hath whereof to glory; but not before God.
3 For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness.
4 Now to him that worketh is the reward not reckoned of grace, but of debt.
5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
8 Blessed is the man to whom the Lord will not impute sin.
2 Corinthians 5:21
For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
Romans 10:3
For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
Phillipians 3:3-10
For we are the circumcision, which worship God in the spirit, and rejoice in Christ Jesus, and have no confidence in the flesh.
4 Though I might also have confidence in the flesh. If any other man thinketh that he hath whereof he might trust in the flesh, I more:
5 Circumcised the eighth day, of the stock of Israel, of the tribe of Benjamin, an Hebrew of the Hebrews; as touching the law, a Pharisee;
6 Concerning zeal, persecuting the church; touching the righteousness which is in the law, blameless.
7 But what things were gain to me, those I counted loss for Christ.
8 Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord: for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ,
9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:
10 That I may know him, and the power of his resurrection, and the fellowship of his sufferings, being made conformable unto his death;
If the moderators will allow this hypothetical question to better visualize repentance for all today, which has nothing to do with any denominations of man, but everything to do with the foundation that all Christian believers are to build upon:
What would be your case to God for Him granting you eternal salvation?
Would you claim that you were a "good" person on earth? Would you remind Him of all the religious doctrines that you followed and obeyed in order to achieve righteousness for Him? Would you tell Him that you "turned from your sins", or that you always asked Him for forgiveness when you were sometimes weak? Would you stress that you followed the earthly ministry of Christ for Him? Would He agree?
I would ask you to repent of this mindset and rather consider this:
Thank God today for what He did FOR YOU, by forgiving you of your sins through Jesus Christ's shed blood on the cross and gifting your eternal salvation through mere belief, and that He did this all by His grace and out of His love.
2 Corinthians 11:3
But I fear, lest by any means, as the serpent beguiled Eve through his subtilty, so your minds should be corrupted from the simplicity that is in Christ.