In the Organic Foods Production Act of 1990, the definition of an organic agricultural product is given as, "produced and handled without the use of synthetic chemicals." Also, "not produced on land on which any prohibited substances, including synthetic chemicals, have been applied during the three years immediately preceding harvest of the agricultural products." In addition, this act contains regulations for certifying operations as organic. See the resources section for a link to a complete text of this Act.
Organic seeds, therefore, are seeds which have been produced entirely through organic practices by a certified organic operation. In order to be sold as such, they must be produced by such a facility which has been certified by an accredited government agency.
Furthermore, most seed producers who claim an organic origin of their seeds will specify whether the seeds have any relation to GMOs (Genetically Modified Organisms) or GE (Genetically Engineered) organisms. Unfortunately, these have no relation to the legal definition of "organic." Most home gardeners who are interested in organic gardening prefer to use seeds free from any GMO or GE strains.
Organic seeds will be clearly labeled as such. For further assurance of a seed's organic origin, look for the official USDA organic seal, which can only be affixed to a product if it comes from an officially inspected facility.
Nearly all seed companies have a selection of organic seeds. Check the individual packages of seeds to be found at your local garden center. Dozens of seed companies sell organic seeds over the internet as well as with mail order catalogs. See the resources section for a link to a site which compiles a list of companies selling organic seeds.