Concise Bible Dictionary:

The idea conveyed in this term is of great importance from the fact of its application not only to man but to God, showing how God, in His government of the earth, is pleased to express His own sense of events taking place upon it. This does not clash with His omniscience. There are two senses in which repentance on the part of God is spoken of.
1. As to His own creation or appointment of objects that fail to answer to His glory. He repented that He had made man on the earth, and that He had set up Saul as king of Israel (Gen. 6:6-7; 1 Sam. 15:11,35).
2. As to punishment which He has threatened, or blessing He has promised. When Israel turned from their evil ways and sought God, He often repented of the punishment He had meditated (2 Sam. 24:16). On the other hand, the promises to bless Israel when in the land were made conditionally on their obedience, so that God would, if they did evil, turn from or repent of the good that He had said He would do, either to Israel or in fact to any nation (Jer. 18:8-10). He would alter the order of His dealings towards them, and as to Israel He said, “I am weary with repenting” (Jer. 15:6). In all this the responsibility of man is concerned, as well as the divine government.
But the unconditional promises of God, as made to Abraham, Isaac, and Jacob, are not subject to repentance. “The gifts and calling of God are without repentance” (Rom. 11:29). “God is not a man that he should lie; neither the son of man that he should repent: hath he said, and shall he not do it?” (Num. 23:19; 1 Sam. 15:29; Mal. 3:6). And this must hold good in regard to every purpose of His will.
As regards man, repentance is the necessary precursor of his experience of grace on the part of God. Two motives for repentance are presented in scripture: the goodness of God which leads to repentance (Rom. 2:4); and coming judgment, on account of which God now commands all men to repent (Acts 17:30-31); but it is distinctly of His grace and for His glory that this door of return to Him is granted (Acts 11:18) in that He has approached man in grace and by His glad tidings, consequent on His righteousness having been secured in the death of Christ. Hence God’s testimony is “repentance toward God, and faith toward our Lord Jesus Christ” (Acts 20:21).
Repentance has been described as “a change of mind Godward that leads to a judgment of self and one’s acts” (1 Kings 8:47; Ezek. 14:6; Matt. 3:2; Matt. 9:13; Luke 15:7; Acts 20:21; 2 Cor. 7:9-10; etc.). This would not be possible but for the thought of mercy in God. It is the goodness of God that leads to repentance (Rom. 2:4).
Repentance is also spoken of as a change of thought and action where there is no evil to repent of (2 Cor. 7:8).

Strong’s Dictionary of Greek Words:

from 3326 and 3539; to think differently or afterwards, i.e. reconsider (morally, feel compunction)
KJV Usage: