Clement Greenberg was an art critic who could make or break your career based on what he said about you and whether or not he liked your work. In my opinion, he was a total jerk, but that's not really relevant to what I'm going to talk about today.
According to Greenberg there were two types of art: avant-garde and kitsch. Kitsch is crappy art. It's art that hands you everything you need to know about it on a silver platter, whereas avant-garde is art that is autonomous. (Autonomous art makes you think, it challenges your brain and doesn't hand you anything. You have to come up with what you think it's about all on your own. It's hard. It's not fun. It's not enjoyable, per se, either.) But Greenberg isn't the first to come up with these ideas about art, instead he bases a lot of his opinions off of Theodore Adorno.
Adorno lived in the 30s and he saw the Nazi's rise to power, he knew where communism was headed, and he knew that none of this was good. All these political debates were producing lots of kitsch-y art. Political propaganda was rampant everywhere - even the United States. This political art is geared toward the public, for the masses, and it doesn't want you to think for yourself.
Heaven forbid mass public have their own thoughts! You must only think in the way of the Fuhrer!
This disgusted Adorno. He believed that art should not be political. Art should be about art and not politics. Politics are a part of mass culture, and really great art should stand a part from everything else - that's what makes it avant-garde. Not a lot of people can really understand it, but it makes you see that you don't have to be a sheep - autonomous and avant-garde art make you think, it makes you realize that there is something out there bigger than just what your political leaders want you to think. It's keeping hope alive that we don't all have to wear grey flannel suits.
It's because of Adorno's ideas, that Greenberg is so interested in the avant-garde and being ahead of society. Because the avant-garde isn't really completely understood by a lot of people (hence the whole being ahead of society bit), the mass culture relies on critics (like Greenberg) to tell them what it's all about.
(I think that's really sort of ironic, if you think about it.)
But also, the more and more people that were understanding this new art, the less avant-garde it becomes. Which means that art must keep progressing, it must keep up with being un-understandable to the masses so that we can keep believing that we don't have to be handed all the answers.
And that's why Greenberg could make you or break you as an artist depending on what he wrote about you. If your stuff is complete kitsch (think Thomas Kinkade) then why should anyone pay attention to you? But if your artwork is avant-garde (think Jackson Pollock) then boy oh boy were you one of the most amazing artists ever and everyone should buy your creations.