Think about it like this (I find this analogy always helps people). Suppose I had this color bar representing an evolutionary lineage:
Now suppose I asked you to draw a line between red and orange. Where you draw the line and where I draw the line will probably be at two different RGB values. The reason being of course, the change from the "red species" to the "orange species" is very subtle--Its not a "click and where there" kind of thing. Rather it is an extremely gradual change in RGB values where a single pixel line (a "generation") is essentially (to us visually anyway) indistinguishable from the next.
Likewise, "species" are the same way. The variation vertically in anyone generation, is typically less than what is found within the population at large. Therefore, from parent to offspring (generation to generation) the distinction between "species" doesn't actually exist.
It only exists because the fossil record is incomplete (for example, we may have many "in between" generations missing between red and orange) and we are observing it in hindsight. Because of the incompleteness artefactual "divisions" can exist in a lineage--Which we call "species".
Consider another thought experiment put forth by Dick Dawkins. Which addresses the problems with the "biological species" concept and evolutionary lineage historicity.
Suppose you and I have a time machine and were off to collect historic ancestors in a manner rivaling the Victorian rape of the natural world. The ol' snatch and grab.
Suppose we dial our flux capacitor back to 10,000 BC and hop back through time.
[PLAIN]http://t1.gstatic.com/images?q=tbn:ANd9GcQV9wpCBWK5jCOo40cAhCAx22KahbsY6xfZA-TFxbD3zD3Rc1vYyQ
Abducting a person then bring them back to our future. In our sick experiment, we convince a modern individual to breed to this person from an ancestral population and see what happens.
Probably, we get offspring. So according to the biological species concept (we can interbreed--Simplified) we are of the same "species" as the individual from 10,000 BC.
No suppose we repeat our foray into history many times, hopping back in 10,000 year intervals. Eventually we run into an individual, well call individual X that cannot interbreed with us. So have we found an objective measure of our "species" its "ultimate origin"?
Consider the individual we abducted before X, we'll call Y. Individual Y, who we
can interbreed with and is therefore "of our species" could very, very likely interbreed with individual X. In other words, individual Y's "X" is not the same as our "X", though both us and Y and still interbreed.
How then, can we have found a finite boundary to our species, when members we consider our "species" can interbreed with those "not of our species", while we cannot?
Species, much to the discomfort of even many professional biologists, aren't real tangible things---Lineages and populations are.