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Population III (Pop III) is a theoretical stellar population, consisting of stars in the early universe formed when there were no metals, thus have no metallicity. Population III stars' (Pop III stars) lifetimes and subsequent supernovae presumably hosted the first substantial nucleosynthesis subsequent to the Big Bang nucleosynthesis. The theory's general motivation is: presuming the Big Bang and the universe's finite age, there must have been some original stars created with primordial abundances. An example criterion used to determine whether a star belongs to Pop III is an iron abundance of [Fe/H] < -6 (i.e., in bracket notation, meaning less than a millionth that of solar). The phrase extremely metal poor (EMP) is sometimes used to indicate something close to Pop III stars, an example criteria being [Fe/H] less than -3. The theory of stellar structure has been used to model the characteristics of stars solely consisting of hydrogen and helium and theories suggest they could be much more massive than any current stars.
The name Population III was inspired by the stellar populations discerned in Andromeda and the Milky Way, for which the terms Population I and Population II were coined for metal-rich and metal-poor stars. I believe the term Population III was coined for such early-universe stars, but the term is also seen for theoretical metal-free stars that might be produced within present-day clouds of extremely low metallicity. Such clouds are unlikely within "normal" galaxies, such as the Milky Way, but would be free gas that has somehow avoided star formation throughout the life of the universe.