There are several programs that certify products as organic, some run by national or local governments and some by NGOs (non-governmental organization, otherwise known as "non-profits"). Organic certification guarantees that the producer has complied with a set of standards such as not using genetically modified seeds, no use of chemical pesticides or fertilizers, etc. For products such as cosmetics, each individual ingredient must be from a certified producer and the container must specify percentage of organic ingredients.
Of course, no system or reality is perfect. As, for example, an organically farmed apple sits on display, it will come into contact with air; even in Antarctica, which has the purest air and water in the world, one can find minute traces of industrial chemicals. Organic certification does not guarantee that no single molecules of chemical pesticide will be present, but rather that certain procedures were followed to avoid deliberate use of non-organic materials and that the resulting product has only minimal (undetectable outside a sophisticated laboratory) quantities of non-organic compounds (i.e. far fewer than found in equivalent conventional products).