The oldest meanings
In the Hebrew tradition the rainbow is a covenant — a promise set in the clouds after the flood. In Norse story it is Bifröst, the burning bridge between the world of people and the world of the gods. In Irish folklore there is gold at the end of it, guarded by someone who does not want to share.
The common thread is that a rainbow is a message: something has been noticed, something has been promised, or a door has briefly opened. Few weather signs carry this much story.
A rainbow on your wedding day
Wedding folklore reads a rainbow as blessing and good fortune — the storm that passed, the promise kept, the bright ending. Photographers love them for more practical reasons: rain-washed air and low sun make extraordinary light.
If one appears at your event, stop and look at it. That is the whole ritual. Folklore will supply the meaning for free.
What the light is doing
A rainbow needs two things: sunlight behind you and rain in front of you. Light enters each raindrop, bends, reflects off the back of the drop and bends again on the way out — which is why the colours always sit in the same order and why the sun must be low for the arc to climb high.
This is also why nobody reaches the end of a rainbow. It is not a place. It is a direction — move, and it moves with you.
Rainbows as weather signs
The old rhyme 'rainbow in the morning, sailors take warning; rainbow at night, sailors' delight' has real logic in mid-latitudes, where weather travels west to east. A morning rainbow means rain to the west — possibly heading your way. An evening one means the rain has passed east.
It is a rule of thumb, not a forecast, but it is one of the better ones folklore produced.
Can you ask for one?
You can ask for anything. A rainbow wants rain and sun at once, which makes it the one piece of weather even a witch hesitates to petition for — the sky must be half-contradicting itself.
Ask for a clearing late in the day instead, with showers passing east. If the sky is feeling generous, the rest arranges itself.