Genesis - Chapter 9

Noah and his family have survived the global flood.  They have finally left the ark.  And God talks to them:

Then God said to Noah and to his sons with him: ‘I now establish my covenant with you and with your descendants after you and with every living creature that was with you – the birds, the livestock and all the wild animals, all those that came out of the ark with you – every living creature on earth. I establish my covenant with you: never again will all life be destroyed by the waters of a flood; never again will there be a flood to destroy the earth.’

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: I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth. Whenever I bring clouds over the earth and the rainbow appears in the clouds, 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. 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.’

So God said to Noah, ‘This is the sign of the covenant I have established between me and all life on the earth.’

Before Noah built the ark, God promised that he would establish a covenant with him (Chapter 6, verse 18).  And Noah was faithful and trusted and obeyed God.  And so the time for the covenant has come.  And God not only gave the words of the covenant, he gave all people a permanent sign of it - the rainbow in the sky.  Whenever we see the rainbow we are reminded of God's covenant.  But we also reminded of Jesus words at the last supper, when he said to his disciples:

‘This cup is the new covenant in my blood; do this, whenever you drink it, in remembrance of me.’ For whenever you eat this bread and drink this cup, you proclaim the Lord’s death until he comes."

The rainbow reminds us of the covenant given to Noah; which reminds us of the "new covenant" in Jesus blood - which reminds us of his death; his resurrection and the promise of his second coming.