The Smell is called "petrichor" (PET-ri-kuhr) noun
The pleasant smell that accompanies the first rain after a dry spell.
[From petro- (rock), from Greek petros (stone) + ichor (the fluid that is supposed to flow in the veins of the gods in Greek mythology). Coined by researchers I.J. Bear and R.G. Thomas.]
"Petrichor, the name for the smell of rain on dry ground, is from oils given off by vegetation, absorbed onto neighboring surfaces, and released into the air after a first rain."
Matthew Bettelheim; Nature's Laboratory; Shasta Parent (Mt Shasta, California); Jan 2002.
(Unashamedly plagiarized from another website - Wordsmith" - check it out!)