Organic just means that that the pesticides and fertilizers are organic as opposed to inorganic. So while a nonorganic farm will fertilize with a mixture of nitrogen/phosphorus/potassium compounds (scary-sounding "chemicals"), an organic farm will fertilize with organic (previously/currently living) material that contains high levels of those chemicals.
That's not what organic means. Technically organic can mean derived from something that is/was living, but it can also mean anything that contains hydrocarbons. Similarly inorganic can mean either something not contained within anything that is/was living (which honestly with how varied life is doesn't cover much), or else something not containing carbon.
That however is the actual definition of organic as opposed to how it's used in marketing material. When talking about marketing, organic just means that a particular subset of approved pesticides and possibly fertilizers, was used in growing the produce. It has no particular meaning beyond that when used as a marketing term. In particular what pesticides are or are not approved is at the discretion of the organization providing the organic certification, so depending on where you are and what group is certifying a product as organic will determine what was used in growing it.
I've started calling it "organic branded" instead of "organic" because it is too vague to have a real meaning, if it doesn't mean the opposite of "inorganic." In common usage the word seems to mean "pesticide free" or "I believe this is healthy." All food is organic, by definition. Not all food was raised without commercial pesticides, or whatever the brand means. Hence, "organic branded" which is precise.
Just to clarify, I was referring to the meaning of “organic” specifically in “organic food”. The way the regulations have defined it is “grown with only non-synthetic or exempted synthesized fertilizers/pesticides/etc.”
This is a totally different meaning than “organic” in “organic chemistry” or “organic compounds.”
It does include synthetic compounds, although the general rule for whats allowed in organic farming (by the FDA, international rules might vary) is synthetic compounds are not allowed and non-synthetic compounds are.