In biogeography, a biological category of living things is said to have cosmopolitan distribution if this category can be found almost anywhere around the world. See "cosmopolitan" for etymology.
An example of a cosmopolitan species is the Painted Lady butterfly.
It is also spoken about, e.g., cosmopolitan genus, cosmopolitan family, etc. A cosmopolitan category is sometimes called simply cosmopolite.
Normally the term is understood in a narrower sense: a cosmopolitan species can be found around the world, but only within the conditions suitable for its habitation. For example, the basking shark is described as cosmopolitan, but clearly it cannot be found in, say, Siberian taiga. So, the term "cosmopolitan tropical" would mean that the species may be found within the tropical zone around the world.
Examples of cosmopolitan species