From our limited perspective, God does sometimes seem to change His mind. When the city of Nineveh repented as a result of Jonah's preaching, for example, the Bible says that God "had compassion and did not bring upon them the destruction he had threatened" (Jonah 3:10).
But that's only part of the picture. The Bible tells us that God is perfect and all-knowing, and even when He apparently changes His mind, He is actually carrying out what He intended to do all along. He knows what is going to happen; nothing on earth ever surprises Him. The Bible says, "I the Lord do not change" (Malachi 3:6). It also reminds us that "Nothing in all creation is hidden from God's sight" (Hebrews 4:13).
What difference does this make? For one thing, it tells us that we can trust God for our eternal salvation. If God was constantly changing His mind, might He not change His mind about us? Might He decide to save us one day, and then reject us the next? But God isn't like that! He has promised us that if we have put our faith and trust in Jesus Christ for our salvation, then nothing "will be able to separate us from the love of God that is in Christ Jesus our Lord" (Romans 8:39).
It also means we can trust God with our lives right now. God loves us, and He has a plan for our lives. No matter what we face in life, He is with us and will never abandon us. Thank God for His unchanging love!