A rainbow baby is a (miracle) baby conceived after the loss of another child. 

"Rainbow Babies" are the understanding that the beauty of a rainbow does not negate the ravages of the storm. When a rainbow appears, it does not mean that 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 the clouds. Storm clouds may still loom over but the rainbow provides a counterbalance of color, energy, and much needed hope.