Which characteristic must a food have to receive a “natural” label by the fda?

produced on a farm with renewable resources

free of artificial ingredients

raw

unprocessed

 it has to have no artificial ingredients 

I would say free of artificial ingredients like say food coloring or monosodium glutamate or aspartame so that it is unadulterated and only contains naturally occurring ingredients like say egg, or fresh vegetables or chicken broth, for example.

You did not show us the image of the burger, but i shall try to answer as best i can.  when purchasing food, always consider the ingredients as well as the person who prepared it. consider if they were hygienic people or not, in case the burger was infected with bacteria. no mortal should place an infected burger into their mouth.