Google the phrase and you'll get 34 million results. You'll find just as many definitions of "clean eating," making the phrase itself ambiguous.
To me, the clean eating movement highlights the ignorance of the average consumer regarding agriculture, food science, nutrition and health.
I am grateful for the science of modern farming, and the advances in food science that allow me to enjoy my food. I like that my loaf of bread stays fresh long enough for me to eat it (because of preservatives) and that it is fortified with B vitamins, calcium, and folic acid. I also appreciate that GMO's, herbicides, pesticides and fortification techniques allow us to better feed the world. The Golden Rice Project has helped address the issue of vitamin A deficiency that causes irreversible blindness and kills approximately 2 million people each year, many of them pregnant women and children.
So are you by default "dirty" if you don't eat "clean?" NO. There is nothing in processed foods, non-organic foods, or any other food for that matter that is going to harm your body.
All foods are perfectly acceptable when consumed with balance and variety according to your body's inner wisdom.