What does Genesis 9:16 mean?
Repetition, in ancient literature, was a sign of certainty or emphasis. To repeat the same idea more than once in a row served to establish it as a strong point. This verse restates the same information given by God in verses 14 and 15, with slightly different language. This language is typical of God's relationship with mankind: speaking in human terms for our understanding, though God is above some of the ideas being presented. Symbolically then, when God "sees" the rainbow in the clouds, He will "remember" His everlasting covenant with every living creature of every kind on earth. While God does not need to "see" the rainbow or "remember" His agreement, these words clarify that the rainbow is meant for our reassurance.This verse adds the word "everlasting" to the description of the covenant. This is a unilateral agreement on God's part, and it is not a casual one. It does not depend on the faithfulness of humanity or the animals or anyone else to keep the other side of the agreement. God will do it. Period. He will not send a global killing flood. Ever.
Symbolically, the rainbow will always remind God of His promise. Literally, it is meant to remind us as well.