I've always assumed it's a reference to the prototype theory of concepts, which holds that for each concept, there's some instance of it that feels more typical or "central" than others. E.g. dogs and cats feel like more central members of the category "pet" than alligators do. Wikipedia (emphasis added):
Prototype theory is a theory of categorization in cognitive science, particularly in psychology and cognitive linguistics, in which there is a graded degree of belonging to a conceptual category, and some members are more central than others.
I see. I just searched for "central example" on the Stanford Encyclopedia of Philosophy, and it pops up there in tons of results too. Although there still isn't e.g. a page called "Central Example".
Implied by "the noncentral fallacy"? (I'm surprised at the search engine results (Google, DuckDuckGo); I didn't realize this was a Less Wrong-ism.)
It's not a LW-distinctive phrase. Try searching Google News, for instance. It falls out of spatial models of concepts such as prototype theory, e.g. a robin is a central example of a bird while an ostrich is not.
Searching for the phrase on Reddit does turn up a disproportionate number of hits from /r/slatestarcodex. So not LW-exclusive, but maybe unusually common around here. Possibly traceable to Weak Men Are Superweapons:
...What is the problem with statements like this?
First, they are meant to re-center a category. Remember, people think in terms of categories with central and noncentral members – a sparrow is a central bird, an ostrich a noncentral one. But if you live on the Ostrich World, which is inhabited only by ostriches, emus, and cassowaries, then probably
We use it all the time, but I can't find a post introducing it into the community. Google search doesn't seem to think it's a thing.