What is Repentance?

Repentance is a  change of mind  that results in a change of heart and direction.
It is a command given to all men and must be proclaimed in the name of Jesus for the forgiveness of sins.

Repentance is not turning over a new leaf or cleaning up your act.   It is not  doing more good things  than bad.   It is not  joining some religion and  conforming  to their rules and hoping when you die that all your good deeds will earn you Heaven.
One must first realize he cannot save himself nor merit a place in heaven.

God gives us the opportunity to repent, but we still decide to repent.  The evidence of true repentance is a changed life marked by good deeds and the fruit of the spirit.

It leads to salvation if there
is godly sorrow for sin
according to the will of God.

"For godly sorrow worketh
repentance to salvation not
to be repented of: but the
sorrow of the world worketh
death."  2 Cor 7:10

נָחַם nâcham, naw-kham'; a primitive root; properly, to sigh, i.e. breathe strongly; by implication, to be sorry, i.e. (in a favorable sense) to pity, console or (reflexively) rue; or (unfavorably) to avenge (oneself):—comfort (self), ease (one's self), 
a change of mind, as it appears to one who repents, of a purpose he has formed or of something he has done
1.To change one's mind.

2. To change one's mind for better, heartily to amend with abhorrence of one's past sins
There are different meanings of the same word in Greek language.  Also, in Hebrew language.
To care afterwards, i.e. regret
 What is the difference between worldly sorrow and godly sorrow?

Have you ever been sorry for just the consequences of sin, rather than the fact that the sin was evil in the sight of God?  I have.  That is worldly
sorrow.  Just feeling bad about sin does not mean it's godly sorrow.
When we have godly sorrow, we see our sin as God sees it: wicked and deserving of judgment.  We hate it and long for forgiveness from God.

Read Psalm 51 and see how King David wasted away with worldly sorrow
after committing adultery and with Bathsheba and murdering her husband.  After he was confronted with his sin, he came to a place of godly sorrow.  This earnest Psalm of repentance shows how David 
confessed his sin specifically and asked for deliverance from it.
He recognized  that nothing that he had or did could cover or pay for his sin, but all he had to offer God was brokenness over sin and the desire for change- he offered God his repentance.

Psalm 51 Audio Video                                                                          

"Repent" definition Word-Study from the KJV Bible's Built-in Dictionary. Repentance, to repent, repent ye. King James Bible

Repentance in the Bible has three basic elements: a genuine sorrow towards God (II Cor. 7:9-10),

a genuine separation from sin (Heb. 6:1; Acts 26:20), and a genuine submission to God’s will (Acts 9:6; I Ths. 1:9). In other words, repentance involves a totally changed life. II Corinthians 5:17 says, “Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.” According to the Bible, all things are new once a man is in Christ, and old things are passed away. Repentance is certainly a requirement. Jesus began his ministry preaching, “Repent: for the kingdom of heaven is at hand.” (Mat. 4:17) In Matthew 9:13 he said, “. . . I am not come to call the righteous, but sinners to repentance.” He upbraided cities in Matthew 11:20 “because they repented not.” Repentance is required for salvation, and no honest and serious student of Scripture can claim otherwise.

The top photo is from my Websters 1828 Dictionary.. the watered 

down definition sure has changed over the centuries.