Paleo is the philosophy that humans are better off with food made from the ingredients that were available before the advent of agriculture and without ingredients typical of the modern age.
Practically, a vegetable is considered a vegetable and a leafy green is considered a leafy green even if they are modern cultivars and don't look much like their natural ancestors and cousins.
Grains (plant seeds) were eaten by some hunter-gatherers but not by our primate ancestors and never in the amounts that we do today. Practical experience shows that people usually function better without.
Chemical preservatives give rise to cheaper foods because they give a long, room temperature, shelf-life but they have the same killing effect on your intestinal bacteria and those are important for your digestion, general health, and well-being. With refrigeration, pickling, and cooking we can do without in the modern world.
Dairy for adults and teens is a big discussion. Some people use the label primal or paleo 2.0 to indicate that they include dairy. Other people find that even though they aren't lactose intolerant they do not function well with dairy - this often includes people with autoimmune disease or other immune malfunctions.