Stars observed in galaxies were originally divided into two populations by Walter Baade in the 1940s. Although a more refined means of classifying stellar populations has since been established (according to whether they are found in the thin disk, thick disk, halo or bulge of the galaxy), astronomers have continued to coarsely classify stars as either Population I (Pop I, metal-rich) or Population II (Pop II, metal-poor). However, even the most metal-poor Pop II stars have metallicities (commonly denoted [Z/H]) far above that of the gas left over from the Big Bang.
For this reason, astronomers have introduced a third class of star. Population III (Pop III) stars are composed entirely of primordial gas – hydrogen, helium and very small amounts of lithium and beryllium. This means that the gas from which Pop III stars formed had not been ‘recycled’ (incorporated into, and then expelled) from previous generations of stars, but was pristine material left over from the Big Bang. As such, these stars would have a [Z/H] ~ -10 and would constitute the very first generation of stars formed within a galaxy. These Pop III stars would then produce the metals observed in Pop II stars and initiate the gradual increase in metallicity across subsequent generations of stars.
The only problem is that Pop III stars are entirely hypothetical at present. Despite intense searches, no Pop III star has ever been observed. A number of explanations have been put forward to explain this:
Whatever the reason, it is extremely unlikely that we will ever observe a Pop III star and they will remain hypothetical entities. Nevertheless, there are still some astronomers out there on the hunt for them.