If someone describes something as being all the colours of the rainbow, it means it is very colourful.
Jane had some incredible clothes in her wardrobe; they were all the colours of the rainbow.
We saw so many amazing birds in the jungle; they were all the colours of the rainbow.
The phrase chasing rainbows refers to someone who is always looking for something more exciting and rewarding but is unlikely to find it.
John, just enjoy what you've got and stop chasing rainbows!
The colours of a rainbow seen by a human eye are red, orange, yellow, green, blue, indigo and violet.