I think it means slightly different things to different people. To me, it means eating whole real unprocessed foods in as natural a state as you can find them. I don't really use the term much in regards to the hcg phases, but in P2, for me it would mean eating pastured meat, organic fresh vegetables and organic fresh fruit. I wouldn't consider the breadsticks to be "clean" eating, but I do eat them in P2, usually. I would consider them on protocol, acceptable, even encouraged, but not clean.
In P3, for me it means eating pastured meats, eggs and dairy without any additives, organic vegetables, healthy fats like butter, pure olive oil, coconut oil, etc. It means sourcing food carefully and cooking foods yourself from their original state rather than buying food that manufacturers may have ruined either in the growing/raising of the ingredients or in the cooking/processing of the final product. For example, homemade organic raw yogurt is clean. Yoplait or even Fage is not. Cheese made from the milk of pasture raised animals and containing only milk, culture, salt and rennet is clean. Kraft pre-shredded cheddar with whatever junk they add to it and made from the milk of sick cows is not. Snowville cream is clean. Just about any other cream sold at the grocery store (including WF and TJ) with ingredients other than cream and made from the milk of sick cows is not. In P3, I would also not consider eating mug cake or artificial sweeteners or protein powder or baked goods made with coconut flour or almond flour to be clean eating. I often use coconut and almond flour in P4 and would consider it clean at that point, but I don't consider it clean eating in P3.
In P4, it means the same thing as in P3, but with the addition of organic fruit, properly prepared grains/starches, and alternative grain free flours. I try to follow a Weston A. Price Foundation/Nourishing Traditions way of eating. For me, clean is when I'm eating by those principles, which I don't always do.