I've known of this supposed sentence and still can't parse whatever the fuck is connecting the two groups of bullying animals who are both from the upstate NY city.
Yeah, Buffalo has a few less known meanings. One is "to bully" or something.
Of course you also have the animal, Buffalo, which is just a bison IIRC, and then you have Buffalo the place.
So Buffalo (bison) from Buffalo (place), Buffalo (bully), Buffalo (bison) from Buffalo (place).
....Someone else commented explaining the groups, I'm summarizing here.
Anyways, one way to refer to a thing from a place is to put the place before the thing, like "new York pigeons". Aka, pigeons from New York.... But phrasing it with the location first omits the "from", so Buffalo from Buffalo, is simply "Buffalo Buffalo" are bullying (aka Buffalo) "Buffalo Buffalo"... Etc.
This sentence probably worked better at a time when "buffalo" was actually a commonly used verb. It's also made really confusing by using a "reduced relative clause" in a way that almost no native speaker would use it.
You can use a reduced relative clause in ways that aren't at all confusing, like:
"The burger I ate was delicious" vs. with a normal relative clause "The burger that I ate was delicious".
But this one is more like:
"Gazelles lions eat are slow." vs. "Gazelles that lions eat are slow."
I don't know what exactly it is, but that is much more confusing. Maybe because the distinction between the subject (Gazelles) and the relative clause ([that] lions eat) is much less obvious, making it hard to parse.