Its formal name is "petrichor," and it consists of oils and scents plants release upon rain. It's bacterial! Doesn't stop it from smelling so good. :)
It smells fresh. If new life had a smell, it would be petrichor and the clean powdery smell of a baby's skin.
Also related to the smell of rain is the sight of rain at night, and how car lights and streetlights reflect off of it so beautifully.