In the US, any domestic or imported winemaker that wants to use the word "organic" on their label must meet the guidelines of the USDA. The grapes must be grown without chemical fertilizers, pesticides, fungicides, and herbicides, and must not have been impacted by nearby non-organic vineyards. The wine must be produced without added sulfides, minimal manipulation, no artificial flavors, and is often made with wild yeasts. Growers must rely on more labor intensive techniques to properly manage the vine and grape growth to protect from pests and molds.
To receive the "Organic" certification is such an intensive process that many growers and winemakers (especially those who own smaller-scale operations) choose not to apply, even though they follow organic best practices. The best way to find out if your favorite wine would be considered organic is to ask the winery directly.