The meaning of Repentance in the Bible
(From Easton's Bible Dictionary)

There are three Greek words used in the New Testament to denote repentance.

The verb metamelomai is used of a change of mind, such as to produce regret or even remorse on account of sin, but not necessarily a change of heart. This word is used with reference to the repentance of Judas (Matthew 27:3).

Metanoeo, meaning to change one's mind and purpose, as the result of after knowledge. This verb, with (3) the cognate noun metanoia , is used of true repentance, a change of mind and purpose and life, to which remission of sin is promised.

Evangelical repentance consists of (1) a true sense of one's own guilt and sinfulness; (2) an apprehension of God's mercy in Christ; (3) an actual hatred of sin (Psalms 119:128; Job 42:5,6; 2co 7:10) and turning from it to God; and (4) a persistent endeavour after a holy life in a walking with God in the way of his commandments.

The true penitent is conscious of guilt (Psalms 51:4,9), of pollution (51:5,7,10), and of helplessness (51:11; 109:21,22). Thus he apprehends himself to be just what God has always seen him to be and declares him to be. But repentance comprehends not only such a sense of sin, but also an apprehension of mercy, without which there can be no true repentance (Psalms 51:1; 130:4).

See more on the meaning of Repentance in the Bible:
Repentance {International Standard Bible Encyclopedia}

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