Chemistry defines 'organic' as a compound that contains - yes - carbon.  Organic compounds can be synthetic (man made) or naturally occurring. Everyday examples are vinegar, gasoline, alcohol (both the kind we drink and the kind we put on a cut) and the plastic water bottles we all seem to carry around these days. 

Biology agrees with the above definition of 'organic', but includes living entities - such as animals, plants, bacteria, viruses, etc. The term organic is widely used in other disciplines such as business, sociology, computing and the military.

Popular terminology defines 'organic' as items such as food and clothing, in which has nothing synthetic or artificial has been used in the growth or manufacturing, and have not been genetically engineered.

Some Organic Advocacy Groups:

http://www.ota.com/index.html

This is the USDA's label certifying a product is organic.

NOPA (National Organic Program Act) regulates the organic foods industry in the USA. It is enforced by the FDA. Some of it's  international counter parts: Australia NASAA Organic Standard; Britain has the Organic Farmers and Growers Organic Standards and the Soil Association; Canada: Canada Gazette, Government of Canada; European Union: EU-Eco-regulation; Sweden: KRAV; India: NPOP, (National Program for Organic Production); Japan: JAS Standards.