"Rainbow Babies" is the understanding that the beauty of a rainbow does not negate the ravages of the storm. When a rainbow appears, it doesn't mean the storm never happened or that the family is not still dealing with its aftermath. What it means is that something beautiful and full of light has appeared in the midst of the darkness and clouds. Storm clouds may still hover but the rainbow provides a counterbalance of color, energy and hope.
A baby who is conceived after a miscarriage/still birth/infant death. I've seen many people say this, as in describing a "rainbow baby": 'The rainbow at the end of the storm, the light in your life'. The storm being the miscarriage/still birth/infant death & the rainbow being the baby they have successfully carried to term without problems/complications.
