Ah, pardon the jargon. The proposition is that science neither "proves" nor "disproves." One problem with "proof" is that science (mostly) works by induction: Generalizations are made based on limited, specific observations; predictions are generated based on previous experience. But this is problematic. The fact that every swan we've ever seen is white does not entail that every swan is white. The fact that the sun has risen from east to west every day (as far as we know) does not entail that it will do this tomorrow. At least not in the strong sense implied by "proof." But then I've neglected to define proof. A proposition is proved to be true if it's negation is showed to be impossible.
What of disproof? You'd think this is possible. All we need to disprove the proposition "All swans are white" is to find a black swan. However, Pierre Duhem showed that it's really not so simple. Every experiment, every observation, every test involves assumptions. We assume that our eyes are functioning properly, etc. So, when we have a falsification event (e.g., an experiment that allegedly falsifies a hypothesis), we (almost?) never have
to falsify the hypothesis in question. We could blame one of our assumptions. Perhaps we saw wrongly, and it wasn't a black swan, etc.
The history of science contains many cases, which illustrate both problems. I'll describe one to do with the second problem, from the phlogiston v. oxygen theory controversy during the Chemical Revolution. Without going into too much detail, Phlogiston Theory (PT) seems to imply that the calcination
of a metal will lead its weight loss (as phlogiston leaves the metal). As it happens, calcination leads to a gain in weight! So, how did phlogiston theorists explain this phenomenon? Rather than abandoning their theory (which was a very good, very explanatorily powerful theory), theoriests rejected one or more of the following auxilary assumptions that must obtain for the prediction (viz., calcination -> weight loss) to obtain: 1. Phlogiston has positive weight; 2. Nothing is added to the metal during calcination as phlogiston (according to theory) leaves; 3. Processes involving something (positively) weighty leaving and nothing (positively) weighty entering necessarily leads to weight loss. Rejecting 1. and 3. seem silly, but the idea of massless (or weightless, anyway) entities are not ridiculous. Indeed, the idea of entities with negative weight are not all that ridiculous either. And back in the day, some people were ready to reject 3. on the basis on the weight difference between a balloon filled with air and an empty one. Put the former on a scale, and it weights less than the latter. Now we know that this test is flawed (ironically, some of its auxilary hypotheses are false. Most scientists rejected 2. Most people rejected 2., and came up with some pretty fascinating ways to do so.
Fast forward a few hundred years. The existence of sterile castes in eusocial insects were a great thorn in Darwin's side. Did this stop scientists from believing? No, and thank goodness not, because later genetic findings revealed that the existence of such castes was perfectly Darwinian. Too tired to rehash the entire story here, I'm afraid...
Edit: Gah, I think I went too far into tutor mode again...