Immutability means unchangeable. It is the divine attribute of unchangeableness. God said in Exodus 3:14, "I AM that I AM," signifying His eternal sameness and His sovereignty. He cannot change His moral character, His love, His omniscience, omnipresence, omnipotence, etc. God is "From everlasting to everlasting," (Psalm 90:2).
Immutability does not mean that God does not vary. The incarnation is an example of variation. Also, God's attitude toward a person is changed when the person becomes a Christian. For example, the enmity between God and man is removed (Rom. 5:10).
Mormonism denies the immutability of God. It says that God was not always God, that he was a man on another planet who became a God (Mormon Doctrine, by Bruce McConkie, p. 321).