A rainbow baby is, quite simply, a baby born or adopted directly after the loss of a child either in pregnancy or after birth. This term is a simple way to communicate that this new pregnancy follows a loss, and quickly encapsulates the complicated emotions this pregnancy likely brings.
The storm, in this instance, refers to the tragic and traumatic loss of a child and the ensuing grief as you process that loss.
The significance of the rainbow is that life and hope not only can survive such a storm – but that the storm itself is integral to the formation of the rainbow.