The Wikipedia article on history of organic farming has a fair bit of detail and references more comprehensive works.
Short answer: In the 1970s, organic agriculture movements began seeking official status for their products in food and agriculture regulation and marketing. Most of the organic certification designations that are now standard were adopted around the 1990s.
The surge in organic products’ market share has happened mostly within the last ten years, and is partly the cause and partly the effect of the entrance of industrial agribusiness into certified organic agriculture.
Hmm, I thought you were asking about organics in today’s grocery store. You may recall how there were “natural food stores” prior to what has become mainstream.