A puffball is a member of any of several groups of fungus

Fungus

A fungus is a member of a large group of eukaryotic organisms that includes microorganisms such as yeasts and molds , as well as the more familiar mushrooms. These organisms are classified as a kingdom, Fungi, which is separate from plants, animals, and bacteria...

 in the division Basidiomycota

Basidiomycota

Basidiomycota is one of two large phyla that, together with the Ascomycota, comprise the subkingdom Dikarya within the Kingdom Fungi...

. The puffballs were previously treated as a taxonomic group called the Gasteromycetes or Gasteromycetidae, but they are now known to be a polyphyletic assemblage. The distinguishing feature of all puffballs is that they do not have an open cap with spore-bearing gills. Instead, spores are produced internally, in a spheroidal fruiting body called a gasterothecium (gasteroid ('stomach-like') basidiocarp

Basidiocarp

In fungi, a basidiocarp, basidiome or basidioma , is the sporocarp of a basidiomycete, the multicellular structure on which the spore-producing hymenium is borne. Basidiocarps are characteristic of the hymenomycetes; rusts and smuts do not produce such structures...

).