Actually speciation is well defined. What is difficult to pin down is what exactly a species is, which is due to the variety of different sexual reproductive strategies, and the fact that most things in biology exist within a continuum and not strictly partitioned categories. But just because species are hard to define does not mean populations can't evolve, which is the whole argument anyway.
I like to compare speciation to a color spectrum. You can arbitrarily look at two points on a rainbow and say "this is blue" and "this is red," but you'd be pretty hard pressed to draw a precise line dividing each color. So too with species. We can look and say "this is species x" and "this is species y," but the continuum of continual change in populations makes drawing a line at the exact moment when a new species has formed rather difficult.
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