If you split a population in two and put one of them in different conditions with no interbreeding, then over a long time the two groups would have such different gene pools that they would no longer be able to breed to create fertile offspring.
This is because there would be different mutations and selection pressures and so different alleles would be selected due to differential reproductive success causing a change in allele frequency.
This happens naturally in nature as populations become geographically separated, meaning there is something in the way of groups of a species breeding with each other e.g. a river.