The Chrisian rainbow is a symbol of God's faithfulness and his promise to never again destroy the earth by flood. It comes from the story of Noah and the Flood. After the flood, God placed a rainbow in the sky as a sign of his covenant with Noah to never again destroy the earth and all living creatures by flood (Genesis 9:12-16). In Revelation, John saw a rainbow around the throne in heaven:
Revelation 4:2-3
At once I was in the Spirit, and there before me was a throne in heaven with someone sitting on it. And the one who sat there had the appearance of jasper and carnelian. A rainbow, resembling an emerald, encircled the throne. (NIV)