The sentence is unpunctuated and uses three different readings of the word "buffalo". In order of their first use, these are:
The city of Buffalo, New York.
The animal "buffalo", in the plural (equivalent to "buffaloes"), in order to avoid articles.
The verb "buffalo", meaning to confuse, deceive, or intimidate
Marking each "buffalo" with its use as numbered above gives:
Buffalo1 buffalo2 Buffalo1 buffalo2 buffalo3 buffalo3 Buffalo1 buffalo2.
Thus, the sentence turns into a description of the pecking order in the social hierarchy of buffaloes from the Buffalo zoo:
[Some] buffalo(es) from Buffalo [that] buffalo(es) from Buffalo intimidate [themselves] intimidate [other] buffalo(es) [from] Buffalo.
It may help to consider the following sentence, which has the same grammatical structure as the original.
Many things many people say confuse many people.
Other than the obvious confusion caused by the homophones, the sentence is difficult to parse for several reasons:
The use of "buffalo" as a verb is not particularly common and itself has several meanings.
The construction in the plural makes the verb "buffalo", like the city, rather than "buffaloes".
The choice of "buffalo" rather than "buffaloes" as the plural form of the noun makes it identical to the verb.
There are no grammatical cues from syntactically significant words such as articles (again possible because of the plural construction) or "that".
The absence of punctuation makes it difficult to read the flow of the sentence.
Consequently, it is a garden path sentence, i.e., it cannot be parsed by reading one word at a time without backtracking.
The length of the sentence reaches the limitations of human ability to parse structure and meaning.
It can be extended (and go beyond parsability?) to:
Buffalo1 buffalo2 Buffalo1 buffalo2 buffalo3 buffalo3 Buffalo1 buffalo2 Buffalo1 buffalo2 buffalo3
In which the subject and object of the central verb 'balance'. Indeed, for any n >= 1, the sentence buffalon is grammatical.
http://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo