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Stellar populations are classifications of stars based upon patterns of stellar characteristics observed in Andromeda and the Milky Way, including their metallicity, locations, orbits, and dominant color. Stars in other galaxies can be classified by the same criteria, and distant galaxies can be characterized as having a lot of a particular stellar population.
Population I (Pop I or metal-rich stars), on average have more-circular orbits, are located in spiral arms, as a group, show a lot of blue, and have substantial metallicity. They are interpreted as the more recent stars and the substantial blue color is because they still include hot, short-lifetime stars which dominate the produced electromagnetic radiation (an O-type star can be as bright as a million Sun-like stars). The Sun is a Population I star.
Population II (Pop II or metal-poor stars) include stars in the bulge and the stellar halo, have less-circular orbits, and don't show the blue. They are interpreted as an older generation, and their early stars are long gone, leaving less blue. It is presumed that the Pop I stars formed out of the leavings of the long-gone, short-lived of these stars, possibly in a burst of formation triggered by an event, e.g., a galaxy merger.
These show a qualitative age-metallicity relation (AMR). A quantitative relation has been theorized, i.e., that ages could be derived from observed metallicity, but I believe this is not currently considered reliable.
The term Population III (Pop III or metal-free stars) was more recently coined for the presumed original stars in the universe, with no metallicity, whose lifetime and subsequent supernovae presumably hosted the first substantial nucleosynthesis subsequent to the Big Bang nucleosynthesis. An example criterion used to check for one is [Fe/H] < -6 (using bracket notation), i.e., less than a millionth the iron abundance found in the Sun. 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 term stellar population is also used in a more general sense, using it regarding some specific criteria of interest.