The "organic" category came about in the 1970s. Let's go back a couple of centuries for some context. When restaurants arrived in the US at the end of the 18th century, they were by and large for elites. Restaurants were spaces where people could demonstrate their capital, both monetary and cultural. The French haute cuisine that was served in elite restaurants was expensive, but price was not the only barrier to accessing it. Even if one could afford to dine here, one had to know how to interact with waiters, read French menus, and pair different dishes with wine and other dishes. This was the cultural capital needed to access restaurants.
By the 1880s, however, the elite monopoly on restaurants was diminishing. It took fifty years, but within that fifty year period there had been a four-hundred percent increase in the number of restaurants within the United States. Ethnic entrepreneurs are an important part of the story. The end of the nineteenth century saw successive waves of migrants arriving from Europe. Many established their own food businesses, serving fare that the middle-class could - for the most part - afford. Restaurants exclusively catering to the elite sought to target the emerging middle-class market because there was much profit to be made. In order to accommodate the middle-class, many formerly elite restaurants printed their menus in English (French was a language that demonstrated cultural refinement, knowledge that the vast majority of middle-class folks wouldn't have), made their food cheaper, and began incorporating regional American fare onto their menus.
This is where the short answer to your question begins. The restaurant as Americans knew it had been transformed and it underwent another significant change in the 1920s and 30s: technology. Restaurants sought to reduce costs, extensively employing increasingly available canned, frozen, and mass-produced food that was prepared in advance and kept warm in a chafing dish. Seasonal availability was no longer a significant issue after the post-war era; many were happy that they could get their favorite dishes year-round. Alongside increasingly standardized food, restaurants moved towards standardized menus and advertising across their chains, chains that became quite popular post-war. Many would argue that this is when fast food came about. Not everyone was happy with mass-produced foods, though. The 1970s saw campaigns towards healthier restaurants with locally produced foods, a revolution supported by celebrity chefs and organics alike. The desire for categorization of (thanks for the correction) organic food, then, emerged in the 1970s as a way to oppose mass-produced fare.
Haley, Andrew P. "Restaurant Culture." In The Routledge History of American Foodways, edited by Michael D. Wise and Jennifer Jensen Wallach. New York: Routledge, 2016.
Hurley, Andrew. "From Hash House to Family Restaurant: The Transformation of the Diner and Post-World War II Consumer Culture." The Journal of American History 83, no. 4 (1997): 1282-1308.
Johnston, JoseĢe, and Shyon Baumann. Foodies: Democracy and Distinction in the Gourmet Foodscape. New York: Routledge, 2010.