“The rainbow will be seen in the cloud.”

-Noach 9:14

The Zohar (I:72b) states that the rainbow is one of the signs of the future redemption.

Commentators note that the rainbow indicates the purification and refinement that the world underwent by means of the Flood. Before the Flood the clouds were very coarse, thus preventing a reflection of sunlight. Thereafter, however, the clouds became more refined; they reflected sunlight, thus bringing about a rainbow.

This, then, is the connection between the rainbow and the future redemption: The entire world will attain the peak of refinement with the coming of Moshiach.