The lesson shown to me...
I'll preface this by saying that I don't particularly like serrations, I think they're a pain to make, a pain to sharpen, and only useful in about a quarter of the tasks a knife might be called on to do.
That said, I did have the 'point' of serrations (pun intended, apology tendered) explained quite graphically to me. It was done thusly:
My friend Eric was very into cutting and testing everything he made or used. He had therefore had ample opportunity to try various blade designs. His simplest cutting test was to hang a two-litre bottle, filled with water, from a rope. This, while by no means a realistic test, offered a reactive target, which simulated a medium/hard cutting situation.
He had me take my best shot it, using a plain blade. Several of my best shots, in fact. To my embarassment, I couldn't even penetrate the bottle. I would have had more effect if I'd used a hammer. The bottle was scratched, and swung wildly, but not cut through. I was mortally embarassed, until explained a couple of things to me, and I tried a couple of other knives. A knife, he explained, will slash soft tissue, given enough resistance. Against a target that will roll or shift, however, a straight edge is as likely to slide harmlessly off as to penetrate. To heighten the possibility of penetration, he further stated, there has to be some abrupt change in the edge geometry. This he demonstrated with a 'Tanto' tip--you know, that sharply angled tip style so lately all the rage with Tactical knifemakers. It easily laid the bottle open, given a similar slash from me. Serrations, then, he offered, are simply nothing but smaller and frequently repeated changes in the edge geometry, to allow the force of the blade to be focused on an extremely small point, thus overcoming the resiliency of the target, and its natural tendency to shift or roll. Continuing tests with a Spyderco seemed to bear this hypothesis out.
Another example might be to take a tomato. Try cutting it with an edge that has been highly honed and polished smooth. You may find it surprisingly aggravating. Certainly, once the skin is pierced, the remainder of the cut will be effortless. But piercing it initially may give you problems, unless you either cheat and use the point, or have an extremely firm tomato, to begin with.
Finally, having worked in theatre as a flyman and a rigger, I have found that serrated knives are all but useless for cutting hemp rope. The teeth tend to catch in the fibres, but unless you can steady the rope and saw away at it, you'd be better off with a plain edge. Alternately, you might see surprising success with the very shallow, wavey serrations on the average breadknife. I've seen them used by guys hanging upside down, 50' above a stage floor, where there was no other option but to cut it, the first time, with one hand.
My two coppers...