Genesis 8-10
“I will remember My covenant, which is between Me and you and every living creature of all flesh” (9:15). When God “remembers” someone in the Bible, He does so in order to have mercy on them. When Noah and his family and the animals were shut up in the ark, “God remembered Noah and all the beasts …” (8:1), and at that time caused the flood to begin receding.
With the rainbow, God declared that He would always “remember” us, His bruised, broken, fragile creation – men and women, plants and animals alike. And He will not flood the earth again.