The term repent at its root means “to change one’s mind.” To repent of sin means to change your mind about sin. At one time you thought sin was good and acceptable and even fun. When you repent, you see sin as evil and harmful. Any change of mind can be described as repentance.
When the Bible says God “changes His mind,” it is speaking of God in human terms. (The technical term is anthropomorphism.) Of course, God knows all along what He will or will not do, and He never changes His mind because He never gets new information that He has to consider. However, as He interacts with people, He interacts in real time. God does not interact with us today on the basis of the sin that we may commit next month. Today, if we are walking in obedience and fellowship with Him, God chooses not to act on what He knows is coming. Likewise, if we are living in sinfulness today, but He knows we are going to repent next year, God does not treat us as He will next year. He deals with us now, in the situation we are in.
In the King James Version, Jeremiah 26:13, 1 Chronicles 21:15, and Joel 2:13 say that God repented. Specifically, God repents of the punishment that He was going to send, because the people repented. God was sending judgment, but, in response to the sinners’ change of mind about sin, God also “changed His mind” about the judgment. Because of the possible confusion such wording may produce, the NIV translates the term “relent,” which does convey the idea accurately: “Now reform your ways and your actions and obey the Lord your God. Then the Lord will relent and not bring the disaster he has pronounced against you” (Jeremiah 26:13, emphasis added).
On the eternal level, God never “changes His mind.” In fact, Numbers 23:19 says that God does not lie or repent—because He never gains access to new information. But on the level of interaction with humans—from our perspective—He does. Although He knows what will happen before it does, He reacts to us in “real time.” When the situation changes, He changes His actions and His responses to us.