Sales of organic food in the US have grown nearly 20% during each of the last 6 years, and the 2002 release of the USDA's organic label added official weight to organic as a highly desirable class of food. Organic food has been shown to have more nutritional content, and children who eat mostly organic diets have been shown to have significantly lower levels of pesticides in their bodies.
The "USDA Organic" label is the gold standard of organic labeling. There are also many certifiers who have their own labels, and they are generally trustworthy. (For example, "Oregon Tilth" is one of the better known examples of certifier labels.) But there are labels other than organic that get applied to fruits, vegetables, and other products in your food market, and it's important to know what they mean.