Jmat, there is a list here, a few entires are quite similar to buffalo-phrase:
https://en.wikipedia.org/wiki/List_of_linguistic_example_sentences

The one which I'm able to recall now and that isn't in the list is 'oysters oysters oysters eat eat eat'

Ruslan, it's a joke or a trick sentence or a riddle, of the kind enjoyed by people who are very familiar with English and enjoy word games, tricks, curiosities, and obscure meanings. It's a game, like trying to construct a valid sentence that ends in five prepositions.

The sad truth is I can't figure this one out myself. It's got me completely buffaloed. I'm going to just Google for the answer. 

Here it is:

https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo

The article explains it. I'm not sure what Internet sites people in various countries can reach, if you have any problems at all reading it let me know and I'll post more details.

In Merriam Webster, "buffalo" is not shown as a verb http://beta.merriam-webster.com/dictionary/buffalo

I've not heard it used as a verb but of course it may be slang and in use in some parts of the USA, perhaps the Buffalo area!

It reminds me of a bad old joke: what is the difference between a buffalo and a bison?  You can't wash your hands in a buffalo.  

(The joke plays with the pronunciation of "basin", which in some English accents sounds like "bison" - you wash your hands in a wash-hand basin.)

*too

I was unaware of the suburb AND the verb, so I had no chance of solving it without that hint.

Now that I know that I have a chance at solving it. The main problem is the capital letters - if they were on different words I could solve it, but as it is there's one two many "buffalo".