In my opinion it is the single most important piece of computer science insight with the constraint that you only have less than an hour.
I often use binary search as a sort of thought experiment into whether something is "obvious" or not. As a child, I would say exponential growth is the one thing that I developed no intuition for between the age of 1–11. Even now, I regard exponentiation as the one really fundamental thing you possibly won't discover or have intuition for on your own and first see it at school (in contrast to addition or multiplication maybe). And even then, you have to accept exponential growth before you start to "understand" it. Maybe if you are Gauss, it's different for you...
Binary search is also a nice way of explaining counting, specifically the combinatorics thereof. You can write down the numbers [0,...,2^n-1] in binary, and then show how when you halve each time with binary search, you actually are just checking the leading bit (and then discarding it). When you have discarded all the bits in that way, then you have found the position you are looking for.