What does "natural" actually mean?

More and more I see "natural" or "all natural" labels on the slightly-cheaper alternatives next to "organic" products, and I find it somewhat confusing. I know that (for example) tofu does not occur in nature, so obviously "natural" does not refer to the whole product, but to the ingredients. But many common ingredients do not occur naturally in the processed forms that we use either.

Today I saw an ad declaring the "first all-natural burger in fast food". This seems like a pretty specific claim for something so nebulous, so it led me to wonder: What exactly does "natural" mean in the context of food? Are there specific rules, or can anyone slap a "natural" label on anything?