I'm guessing it has to do with the Burning Man but fail to see it's link to New York... Maybe my guess is wrong.
The term "burner community" is sort of a catch all for the people actively participating in the subculture surrounding Burning Man. From the POV Im observing [I live in NYC (born here), age 25], NYC area burners seem to have their hands in all things "underground," possibly due to the kind of people that subculture tends to attract. A lot of recurring parties, art collectives and such that I've personally come across and interact with here, seem to be tangentially or directly related to the burner community.
Seems very interesting. I've recently been to an underground experimental music show in Vilnius. I have to say the music was weird (it's even quite hard to say it was music and not performance art) but the people I met there were all very nice and super interesting.