A single species doesn't split cleanly into two new species overnight, at some identifiable single instant. Speciation, the evolutionary process by which one population diverges into two or more distinct species, unfolds gradually, typically over many generations, as genetic differences slowly accumulate between separated populations. Biologists still need a working criterion to say when that gradual divergence has actually produced two genuinely separate species rather than just two somewhat different populations of the same one, and the most widely used answer centres on reproduction: can members of the two populations still interbreed and produce viable, fertile offspring?
Separation first, divergence second
The most common route to speciation, called allopatric speciation, begins with some form of physical or geographic separation — a population split by a new mountain range, a river changing course, or migration to an isolated island. Once separated, the two populations experience their own independent mutations, their own patterns of genetic drift, and often somewhat different selective pressures from their now-distinct environments, causing them to accumulate genetic differences independently, with no gene flow between them to keep those differences from building up. Given enough time and enough accumulated divergence, the two populations can become different enough that even if they were later reunited, they would no longer be capable of successfully interbreeding — at which point biologists generally consider them to have become genuinely separate species.
Reproductive isolation as the practical test
Reproductive isolation, the inability of two populations to successfully interbreed and produce fertile offspring, is the criterion most commonly used to mark that a speciation event has genuinely occurred, under what's called the biological species concept. This isolation can take several distinct forms: prezygotic barriers prevent mating or fertilisation from happening at all (different mating behaviours, incompatible reproductive structures, mismatched breeding seasons), while postzygotic barriers allow mating and fertilisation to occur but produce offspring that are inviable, weak, or sterile (a mule, the sterile offspring of a horse and donkey, is a classic real-world example of a postzygotic barrier in action). Once reproductive isolation, of either kind, has become complete and stable between two populations, they're generally treated as having crossed the threshold from "diverging populations of one species" into "two separate species," even though the accumulation of genetic difference that produced that isolation happened gradually, without any single defining moment marking the actual split.
What we're still unsure about
The general mechanisms of speciation, including allopatric speciation and the concept of reproductive isolation, are well established and supported by extensive observed and experimental evidence across many species. What remains more genuinely debated among evolutionary biologists is how universally the biological species concept, built around interbreeding, actually applies — many organisms reproduce asexually, and even among sexual species, hybridisation between supposedly separate species does sometimes occur and produce viable offspring under specific conditions, which means the interbreeding-based species concept, while broadly useful, doesn't map perfectly onto every real case, and biologists continue to debate which of several competing species concepts best handles the messier edge cases nature actually presents.
This sits inside Speciation & Reproductive Isolation, one of seven topics in Evolution, one of six domains in Biology, one of seventeen subjects the app can quiz you on.