The colors of the rainbow are red, orange, yellow, green, blue, indigo and violet. The rainbow is stated as a sign of the Covenant with Noah (solemn agreement made between God and Noah) and God's promise to Noah that never again would the World be purified by a Great Flood. This covenant was demonstrated by a rainbow appearing in the sky as a sign He had kept His promise. The Rainbow Christian Symbol therefore represents God's faithfulness and of His pardon of the faithful which derives from the story of Noah's Ark.
Gen. 9:12 And God said, "This is the sign of the covenant I am making between me and you and every living creature with you, a covenant for all generations to come: 13 I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth. 14 Whenever I bring clouds over the earth and the rainbow appears in the clouds, 15 I will remember my covenant between me and you and all living creatures of every kind. Never again will the waters become a flood to destroy all life. 16 Whenever the rainbow appears in the clouds, I will see it and remember the everlasting covenant between God and all living creatures of every kind on the earth."
The Easton Bible Dictionary provides the following definition, meaning and emblem for the Rainbow Christian Symbol in the Bible.
It was appointed as a witness of the divine faithfulness (Gen. 9:12-17). It existed indeed before, but it was then constituted as a sign of the covenant. Others, however think that it "appeared then for the first time in the vault and clouds of heaven." It is referred to three other times in Scripture (Ezek. 1:27, 28; Rev. 4:1-3; 10:1).