Simple enough, once you get it spelled out, so to speak... lol
First, the capitalized Buffalo refer to the city in New York; some of the buffalo are animal, and some have a variant meaning (not common, but not unknown, either). I'll write it out, using parentheses to insert non-essential words that make it more understandable, and brackets for other explanation; if you want to make it easier, re-read it and skip the bracketed info.
Buffalo buffalo [entirely correct inversion of buffalo from Buffalo] (that other) Buffalo buffalo intimidate [variant meaning] (also) bully [another variant] (other) Buffalo buffalo.
The entire sentence is grammatically correct, because no commas are required with a restrictive clause, the word
buffalo has multiple meanings, verbs/adverbs are not required in this particular sentence (reduced relative clause), and the plural of
buffalo is... buffalo.
I love the English language, but it can be crazy sometimes...