I confess, my education in philosophy is a bit patchy. Could you break that down for me?
Let's assume that we can treat science as a single thing, which historically we can't because people often have very different ideas about what science should be and how to do it. But if we assume that all these different ideas are lumped together in a single category called science, then what fundamentally unites them is the desire to produce
universally true statements. That is, statements which don't rely on the particular perspective of an individual, but can recognized by anyone.
Mathematics is a good example. Mathematics is an entirely consistent system which is (or can make a reasonable claim to be) universal. Furthermore, if we know the universals, if we know the rules of mathematics, then we can start to manipulate mathematics to our own ends. Similarly, if we can take nature, with all its complex and chaotic and frightening occurrences, and reduce those phenomena to universals, then we have the ability to manipulate natural forces in a consistent fashion. How much fuel do we need to put in our rocket to get to the moon? If we know the universals, then we can sit down and do the maths and know.
That's the really cool thing about science. It works, or it seems to work.
But universal truth implies something more than just "it works". Any believer in magic or miracles can claim that it works (sometimes). We have staked our entire civilization on this idea of universal truths, and on the ability of science to produce them, and we need to know for sure that they are actually universal.
So how do we know something for sure?
Oh, right..
In very very simple term, that's the "crisis". We have a science that works, but we cannot actually substantiate
why it works. We cannot use science to validate the ability of science to produce universal truths, because that would be circular.
On an everyday level, that doesn't really mean much. But it does mean that we should be mindful of the limitations of scientific knowledge, and skeptical of the way "science" is used in a political or aesthetic context, because the colloquial use of science is often completely divorced from any of the things which make science useful. Science can be the maths that takes you to the moon, but it can also be purely an aesthetic convention. It can be a kind of magic dust you can sprinkle onto any statement to make it
sound truthful, and that is potentially very dangerous.