What does Genesis 9:10 mean?
Prior to the flood, God promised to establish a covenant with Noah (Genesis 6:18), after Noah demonstrated obedience by building the ark. In the previous verse, God revealed to Noah and his three sons that He was about to establish His part of that covenant. This agreement would apply to all living things, which were descended from those who left the ark. A "covenant" is a special type of contract between two parties. In this case it is between God and all of humanity.What this verse reveals is that the covenant is also between God and all of animal-kind: every kind of creature that survived the flood aboard the ark. God lists them: birds, livestock, every kind of beast, every living thing. God does not generally make covenant agreements with animals. Yet He gives animals special honor here by including them in this promise. God shows that, though He wiped out nearly all of animal-kind in the flood, He still cares deeply about these creatures He has created. God has said that man will triumph over the animals and that humans may eat anything that moves, but that doesn't mean that God sees animals as worthless or expendable. He makes this promise to them, as well.
The promise, given explicitly in the next verse, is that God will never again destroy all life on earth with a flood.