What does Genesis 9:9 mean?

A "covenant" is a solemn agreement between two parties, where each side has certain obligations. Both parties in the covenant are bound to follow through on their end of the agreement. In some cases, those responsibilities are conditional. In such instances, the requirements are stated as "if this, then that." In others, the mandates are expected no matter what the other party does. In Genesis 6:18, God promises to establish a covenant with Noah. Noah's side of that binding agreement came in his work of building the ark.

Now, as promised, God is about to explain His part of the covenant He has made with humanity through Noah and his sons. God reveals His covenant to all four men and not just to Noah, the patriarch. This will be a covenant with all of the peoples of the earth to follow from these four men—which means it is a covenant with all the peoples of the world to live since that day.

Specifically, God will promise to never again destroy all life on earth with a flood. As a sign of this promise, God provides the rainbow.