Whether species is a concept, or whether it has reality independent of our classification systems, is also subject to debate. Answers to this question may hinge on one's understanding of epistemology as much as of biology.
That species change over many generations is now a cornerstone of biological thought. Prior to Darwin, species were viewed as being a 'type' of organism, with individual differences simply being deviations from the true type. After Darwin, the idea of a true type was rejected, as individual variation was recognized as the raw material of evolutionary change. Differences between individuals could no longer be dismissed as 'imperfections'.
The rise of a new species from a parental line is called speciation. There is no clear line demarcating the ancestral species from the descendent species.
Compare with race.