Just What is a Species?

Nice piece here today about hybrids, animals born of a mating between two different species (a chimera is the technical term, isn't it?). You do want to look at the photo set: the Liger is very fluffy indeed.

However, there's something that confuses me:

Kekaimalu the 'wolphin' was the result of the union of a bottlenose dolphin and a false killer whale, which is actually a member of the dolphin family......Unlike most hybrids, which tend to be sterile, Kekaimalu had two female calfs, both sired by male bottlenoses.

As with one of the other examples, a domestic dog/wolf crossbreed (and I've known a couple of husky/wolf crosses myself) my confusion comes from just what is the definition of a species.

We know that we can cross a horse with a donkey to get a mule but mules are sterile: indeed, that's where we get the meaning of "mule" for sterile from.

But I was taught that if animals from different species could in fact cross breed to create fertile offspring, that this meant that they were not in fact different species. Different looks, perhaps, different sub-species perhaps, but the very fact of fertile offspring showed that they were indeed the same species.

So has the definition of species changed since I was taught that all those decades ago?