rainbow

This is the multicolored arc of light that often appears in the sky after a rainstorm.

a sign

A sign is something (such as an object or event) that gives a certain meaning or which points to something that is true or will happen.

In some languages it may be better to say, "to show that he had promised."

Make sure it is clear that this means every time a rainbow appeared from that time on. It may be necessary to add, "From then on, every time."

This refers back to the previous frame in which God promised to never again destroy the earth with a flood.

These references may be slightly different in some Bible translations.