When the ground and plants are warmer, you can smell something. What you are really smelling comes not from the air, but the ground! Plants release oils that enter the soil and blend with the other earthy odors. These odors are released into the air when the relative humidity at ground level exceeds 75 percent.
Moist humid air will transmit odors far better than dry air. In these moist humid conditions we notice these odors more readily. And since rain is so often connected with moist humid air, we tend to associate one with the other.