Hi Lyn!
For me, the term means avoiding highly processed foods, high glycemic index carbs and industrially-produced meat & dairy products.
I try not to eat the following (or any foods that contain them):
white flour, white sugar and white rice
corn syrup, high fructose corn syrup and other corn-derived food additives
industrially-produced fats and oils
industrially-produced meat and dairy products
white potatoes
artificial sweeteners
hard alcohol
I do eat the following:
fruits, vegetables and legumes of all kinds, organic wherever possible
organic/free-range/grass-fed meat and dairy products of all kinds
wild-caught fish & seafood of all kinds
whole grains of all kinds (and flours derived from them)
nuts and seeds of all kinds (and natural oils derived from them)
natural sweeteners (raw sugar, molasses, honey, agave nectar, stevia)
wine & beer
The 101 Cookbooks site is a great resource for information about and recipes emphasizing natural foods. . . here is a link to the section that discusses building a natural foods pantry.
http://www.101cookbooks.com/build_a_natural/
I do use a limited amount of white flour and white sugar in baking, and I really like a few products that fall outside the above guidelines (Arnolds whole wheat sandwich thins, La Tortilla Factory low-carb/high-fiber tortillas and Wheat Thins fiber select crackers come to mind), but I succeed in adhering to the above guidelines 90% of the time when I'm eating at home/doing my own cooking.
When I'm traveling, eating in restaurants or at the homes of friends, it is much more difficult - I still avoid fast food, packaged snacks and packaged sweets, but otherwise just try to make a reasonable choice from the available options.