Video shows a mushroom that releases spores UP into the air when the surface of the cap get hit with falling water (from a hose here, but rain in nature). The spores are the brown, smoke-like material being given off.
I don't know the name of the fungus, but GUESS that it's in the Phylum Ascomycota, fungi that are "spore shooters."
Below is a photo of another of these fungi that were growing in the mulch next to my home in upstate NY. If you know the name of this organism please email me!