To expand on Jolene's answer, there is not only no official definition, but the only definition which fits its common usage is
A food which a certain group of persons is not afraid to eat.
Philosophically, "natural" is the opposite of "artificial" or "man-made", but philosophy doesn't give us a limit of interaction under which something stays "natural. Does a ear of corn stop being natural when you pick it? When you remove its leaves and silk? When you mill it into cornflour? When you make HFCS out of the cornflour? Somewhere along the process, it becomes "unnatural" as the term is commonly used, but there is no technically obvious place for placing the turning point.
There are three possible ways to define "natural" which would make it more or less objective, but they don't cover the word as it is used in real life, even though there is overlap. Besides, if one of them were the "correct" definition, the commonly assumed connection to "healthy" or "better quality" would not automatically follow from any of them.
The first candidate definition is to say that non-processed food is "natural" and processed food is not. But there are many counterexamples to it. For example, I've seen many foods listing "natural fruit sugar". Well, the fructose in them is processed to about the same level as the sucrose in the competing products, but I've never seen somebody include white refined sugar in their mental list of "natural sweeteners".
Another candidate would be "synthetic", as in chemically synthesized by man as opposed to extracted from an organism which produced the molecule. It would have the advantage of being consistent with the use of "natural" in textiles, another major area of everyday life. Again, this is not congruent with real world usage - a sizable proportion of food additives, which in my experience scare the average natural-eater, are extracted from plants and bacteria, for example xanthan or MSG.
The third possible definition (added after Steve Jessop's comment) would look at human history, draw a limit somewhere and say "these foods are natural, the others are a product of civilization and thus unnatural". As pointed out in the comments, this is indeed used in some nutrition theories such as Paleo. But when we ask ourselves where to draw the line, we'll notice that the average person talking about "natural" food is not as radical as the Paleo people, and will see a loaf of whole wheat bread as a very natural food. Could we find a point in more recent history which supports such a division? It's hard, as technology has evolved in a continuous way, but the best candidate would be the Industrial revolution, amounting to a rapid switch from low-tech to high-tech. Still, if we apply this definition, we see that foods like smoothies or baking soda would fall on the "unnatural" side. But in common use, baking soda has an old-fashioned feel and, if we look at cleaning methods, is often touted as a "natural" alternative to purpose-created cleaning products. So, this definition again doesn't explain the common observations.
"Natural" is an ideological construct common in our society. As with other ideological constructs, its true meaning is determined by who is saying the word, and what his attitude to the object of speech is. As far as I have observed it, it is not connected by any physical properties of the object, at least not in a consistent manner. This is also why there is no definition by the FDA, and there cannot be one either, at least not one which covers the current use.
Note that despite the condescending tone above, I also prefer eating an apple over eating a mix of fructose, water and processed fibre, just like the people who insist on "natural" food. I fully appreciate that having a term which helps us decide the relative "healthiness" of a food would be useful for society. It's only that "natural" isn't that term, even though people insist on using it that way.