Well, God being immutable means that He does not change, which is a remarkable attribute. Systematic theologies, it would be identified as an incommunicable attribute because it finds no expression in the creature. We are changeable. We change every day. We grow taller or we go from a state of being happy to a state of being sad and things about us change.
It's not that way with God. God is unchanging and that means for us glorious things. We don't have to be afraid that he's going to wake up tomorrow. He doesn't do that kind of thing and somehow feel different or be different than he was the day before. God is the same yesterday, today, and forever.
That means His promises are true. And as fleeting as our own emotions are, and as shifting as our own lives are, it brings great comfort to our families when we think that God is the same. He really is not going to change. You