For Jews and Christians, the rainbow is a symbol; a symbol of a promise made by God:
I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.” God said to Noah, “This is the sign of the covenant that I have established between me and all flesh that is on the earth.” (Genesis 9:13-17, ESV)What many people forget is that the rainbow is a symbol of something else:
Now the earth was corrupt in God's sight, and the earth was filled with violence. And God saw the earth, and behold, it was corrupt, for all flesh had corrupted their way on the earth. And God said to Noah, “I have determined to make an end of all flesh, for the earth is filled with violence through them. Behold, I will destroy them with the earth.” (Genesis 6:11-13, ESV)It might be a good idea to remember that.