Roughly, it means, "pushing the boundaries of culture forward."
Of course, it's derived from the military term "vanguard" as has already been described in other posts.
all I have time for at the moment is wiki
http://en.wikipedia.org/wiki/Avant-garde
The origin of the application of this French term to art is still debated. Some fix it on May 17, 1863, the opening of the Salon des Refusés in Paris, organised by painters whose work was rejected for the annual Paris Salon of officially sanctioned academic art. Salons des Refusés were held in 1863, 1874, 1875, and 1886.
Avant-garde represents a pushing of the boundaries of what is accepted as the norm, or the status quo, primarily in the cultural realm. The notion of the existence of the avant-garde is considered by some to be a hallmark of modernism, as distinct from postmodernism. Postmodernism posits that the age of the constant pushing of boundaries is no longer with us.
Postmodernism posits that avant-garde has less applicability (or no applicability at all) in the age of the postmodern.