What is the clearest explanation of what computer scientists mean by "the naive implementation"? I need a good clear example which will illustrate — ideally, even to non-technical people — that the naive implementation may technically be a functioning solution to the problem, but practically be utterly unusable.
I'd try to keep it away from computers altogether. Ask your audience how they find an entry in a dictionary. (A normal dictionary of word definitions.)
The naive implementation is to start at the very beginning, and look at the first word. Oh, that's not the word we're looking for - look at the next one, etc. It's worth pointing out to the audience that they probably didn't even think of that way of doing things - we're smart enough to discount it immediately! It is, however, about the simplest way you could think of. (It might be interesting to ask them whether they can think of anything simpler, and check that they do really understand why it's simpler than the way we actually do it.)
The next implementation (and a pretty good one) is to start in the middle of the dictionary. Does the word we're looking for come before or after that? If it's before, turn to the page half way between the start and where we are now - otherwise, turn to the page half way between where we are now and the end, etc - binary chop.
The actual human implementation is to use our knowledge of letters to get very rapidly to "nearly the right place" - if we see "elephant" then we'll know it'll be "somewhere near the start" maybe about 1/5th of the way through. Once we've got to E (which we can do with very, very simple comparisons) we find EL etc.