What man calls civilization always results in deserts. Man is never on the square – he uses up the fat and greenery of the earth. Each generation wastes a little more of the future with greed and lust for riches.”
Don Marquis
Ah, now it makes more sense!
"...the fat and greenery of the earth."
"The fat of the land" is a phrase that means "living well; fed by abundant crops" (see
HERE )
Although I've never heard "the greenery of the land/earth" I can imagine that it also refers to the vegetation of the planet, used either for food or other practical uses.
So the sentence means that man (ie human beings) use all the available resources of the planet, regularly leaving behind a desert.