From time to time, customers ask us if our honey is organic. As applied to food, "organic" generally means that the food was grown without any synthetic inputs, such as pesticides, herbicides, or chemical fertilizers and was also harvested or processed without any solvents, irradiation or dyes. To be "Certified Organic" or "USDA Organic" there are strict regulations (including extensive record keeping) that must be followed. Penalties and fines can be imposed on farmers and packers for violating these rules and mislabeling products.
For crops grown in a specific place, farmers can control their chemical inputs and harvesting methods and therefore meet the certification requirements. Bees, however, do not remain in a defined area. Bees will generally forage in a 2 or 3 mile radius around the beehive. So even if a beehive is located in the middle of an organic farmer's field, nothing stops the bees from crossing into a neighboring field where chemicals might be used. And because of the pervasive use of agrochemicals in the USA, except for very remote areas of the country, foraging bees are going to come into contact with chemical residue and bring it back to the hive. Thus, unless the bees are foraging in a very isolated area far from any modern farming operations, organic honey is pretty much impossible to get. If anyone tries to sell you "organic" honey, then you should ask if they can prove it.
For more information, see this 2011 article from Scientific American: "Organic Honey is a Sweet Illusion."