The word "organic" and better yet "certified organic" means a product meets certain environmental standards. Anything labeled "certified organic" must be approved by the USDA. Organic mostly refers to raw materials that are grown, produced, and processed without the use of toxic chemicals like pesticides and artificial growth agents. No harsh chemicals may be used in the processing of those materials either—that means the cleaners or dyes that are used must also be certified organic. US law requires that all mattresses must be flame retardant (treated with borate acid), so in order to order a chemical-free non-toxic mattress, you will need to provide us with a doctor's note.
On the other hand, making a mattress completely organic can be expensive. "Green" or "natural" products are those that have not been bleached or altered in any chemical way. Many companies opt to simply make their products more natural, swapping out some chemical ingredients for environmentally-friendly ones. Green products are often made with organic ingredients, but must also incorporate environmentally sensitive manufacturing and operational practices to be truly "sustainable".