If you read Origin of the Species, that was really Darwin’s first step, casting doubt on the traditional notion of species, so that he could redefine the term to suit his purposes. Without that step, his entire theory collapses in on itself. Most people just breeze right past that section without noticing the ramifications of what he did, though.
In fact, there was no strictly defined notion of "species", and indeed there is still not one today.
Humans have always bred and selected domesticated animals to suit our purposes, and so have long known of species' variability.
We've also known that some species cannot successfully interbreed with other -- the example of horse and donkey come to mind.
But the word "species" is strictly a modern construct, whose definitions have changed over time, and is even now changing to accommodate the latest in DNA analyses.
Thus, today a population can be designated a separate "species" even if it can successfully interbreed with others, but ordinarily does not.
If populations are biologically unable to interbreed, in the wild, they are considered not just separate "species", but also separate "genera".
Thus the example of polar bears and brown bears.
Until recent years polar bears were considered a separate genus from brown bears, but since we've seen confirmed examples of polar/brown bear interbreeding, they were reclassified as just separate species.