Organic \awr-GAN-ik\ , adjective;
1. Of, relating to, or affecting organs or an organ of the body
2. Of designating carbon compounds
3. Of, relating to, or derived from living organisms
4. Using or produced with fertilizers of animal or vegetable matter, using no synthetic fertilizers or pesticides
5. Free from chemical injections or additives, such as antibiotics or hormones
When exactly this word was first attested is a bit fuzzy. It definitely dates to at least the 1510's, but it may have been as early as the 1300's. Ultimately the word comes from Latin organicus, which is taken from Greek organikos ("of or pertaining to an organ"). Organikos comes from organon ("instrument") which derives from Proto-Indo-European *werg-ano-, from the base *werg- ("to do").
If those earlier attestations are to be trusted, organic may have actually entered English via Middle French organique or Old French organice, both of which were the name of the jugular vein.
The definition "from organized living beings" is first attested in 1778 and the agricultural sense of "free from pesticides and fertilizers" dates to 1942.