What does Genesis 9:15 mean?

This completes the thought begun in the previous verse. God has established His covenant promise with all life on the earth that He will never again bring a global flood to destroy every living thing. Now God says that when the rainbow becomes visible against the clouds, He will remember His covenant. He will not send another flood.

Usually in Scripture, signs for covenants are given by humans, not by God. Those signs, such as circumcision (Genesis 17:11), are meant to demonstrate the commitment of people to the covenant and to remind them to hold to the agreement they have made. In this case, though, the sign is given by God and it is to serve as a reminder to God of the agreement He has made.

It's an odd idea, to us, that God would somehow need to be reminded of His agreement. He doesn't need to have His memory jogged, of course, but He claims the right to be reminded anyway. This is similar to the reason why God, who cannot lie or change (Numbers 23:19; Malachi 3:6), speaks of "covenants" in the first place: to emphasize to mankind the serious nature of His promise. And while God says that the reminder is for Him, it's also true that the appearance of the rainbow is a reminder to humanity of God's covenant promise, of His grace and mercy to all life on the earth.