OK, the votes in the comments to the Explain This! post came out with NMR/MRI as the clear winner, with a strong plurality wanting to make sure that Fourier transforms are part of the explanation. So that's what I'll take on, but it's not going to appear this week. I'm going to try to pitch the explanation to an intelligent lay reader who doesn't have any particular physics, chemistry, or math skills. I'm out of my mind.
In second place were various suggestions about X-ray crystallography, and perhaps that'll be topic number two. Chirality would be tied with that, except there were actually more votes against it than for it, with people finding it not all that hard to explain. (They've clearly never tried to explain to someone whose specialty is running a Morris water maze assay why all the compounds flipped from R to S just because a group changed out on the far end of the molecule). Other multiple-vote getters were Woodward-Hoffman/FMO, structure determination in general, and antibiotic resistance.
Many of the single-vote topics would be good as well, and some of them would be quite tricky. The person who suggested point group symmetry, though, brought back some memories. I'd never covered anything in that area as an undergraduate, for one reason or another. So there I am in my first year, taking an optical spectroscopy class, and on about the second day the professor launches into a discussion of symmetry operations and their relevance to infrared absorption bands (which is considerable).
And this was the first lecture I had ever heard where I understood nothing but the common verbs and the minor parts of speech. I listened to the whole thing with mounting alarm. It had taken me all the way to graduate school to come definitively to the limits of my knowledge, but the pavement ran out right there. I was so stunned I couldn't even take notes - I'd never tried to take notes on something that I wasn't comprehending at all, so I didn't know how.
That evening, I stalked over to the chemistry library and checked out, among other things, Harry Gray's book on group theory, renowned as the first one on the subject "that you could read in bed without a pencil in your hand". And I didn't go to bed myself until I understood just what I'd been listening to that morning, because I didn't enjoy the experience one bit, and wanted to make sure that it never happened again.