There are two classifications of "organic" foods:
Organic food certified by the Soil Association as "organic" - This means that the Soil Association (a not-for-profit organisation) has certified that the product was produced without the use of additives, pesticides, hormones, chemicals not of an organic nature, and, in the case of animals, was allowed to roam free and eat natural food. It also certifies, in an indirect nature, that the animals were taken good and humane care of. Certified foods, however, are allowed to have one or more "certified" non-organic components, and it is possible to have "organic farmed fish", even though it is impossible to have farmed fish of any type that can be said to have been grown naturally.
The traditional definition of "organic food" is that the product is of a wholly natural origin, and was grown without the use of chemicals that are not wholly natural and organic in origin. This means that free-range cattle would not be organic (since they are immunised and often juiced), but game meat would be, since most commercially reared animals (in particular cattle, chickens and fish) are immunised, and fed antibiotics in their feed. Processed food cannot be said to be organic, with all due respects. You can look through
Gardian | Wales Media : News Resource for some arguements why the Soil Association's rating are considered to be dubious.
The benefits of truly organic food are numerous. It has more vitamins, a higher density of phytonutrients, less contaminants and carcinogens (dnp, ddt, plastics) etc. Basically, you need to eat 3 to 10 times the quantity of mass-produced food to get the same effect as eating one unit of truly organic food. This is more so if the food is of North American or European origin. In that respect, even organic food is not created equal - the higher the quality of the soil, and the shorter the time it has been farmed, the better.