A specific term can be used for the scent or smell present in the environment during the rain. This is "petrichor", which is derived from a Greek word and first of all was used by two Australian researchers Bear and Thomas in 1964.
This sweet smell of wet soil is due the presence of a group of filamentous bacteria known as Actinobacteria, which grow in slightly moist or damp soil. When the conditions are dry this bacteria start producing it's spore. As the rain hits ground these spores are thrown up in the air where they get mixed with moisture. These spores with moist air have a characteristic smell. It is reported that Actinobacteria also produce a compound geosmin which is a metabolic by product of the same and this compound is responsible for the pleasant earthy smell after rain.