Your first question was to define what organic farming means. The definition given by the United States Environmental Protection Agency is
"Organically grown" food is food grown and processed using no synthetic fertilizers or pesticides. Pesticides derived from natural sources (such as biological pesticides) may be used in producing organically grown food.
Most places organic food is certified, the rules varying by region.
Your second question was does organic farming produce food with less heavy metals? The answer is no.
Organic Food: Buying More Safety or Just Peace of Mind? A Critical Review of the Literature
Faidon Magkos, Fotini Arvaniti, Antonis Zampelas
Critical Reviews in Food Science and Nutrition
Vol. 46, Iss. 1, 2007
Chemical contaminants in food that result from general environmental pollution [cadmium (Cd), mercury, copper, arsenic, zinc, lead, dioxins, polychlorinated biphenyls (PCBs), radioactive nuclides, OCPs] are also potent and may pose serious acute and/or chronic health risks
It is generally accepted that persistent pollutants in the soil such as chlorinated hydrocarbons and certain heavy metals cannot be avoided through organic farming practices.
most studies indicate similar levels of contamination by these pollutants in a variety of both organic and conventional food products; where differences have shown up, they don't consistently give the edge to either type of food (Lecerf, 1995; Woese et al., 1997; Worthington, 2001; Slanina, 1995; Kumpulainen, 2001; Jorhem and Slanina, 2000; Malmauret et al., 2002). It may be that the variability within a given crop is greater than the variability between one cultivation system and another (Jorhem and Slanina, 2000).
Contaminants in organic and conventional foodstuffs in France
L. Malmauret, D. Parent-Massin, J.-L. Hardy, P. Verger
Food Additives and Contaminants
Vol. 19, Iss. 6, 2010
The aim was to compare the levels of contamination in organic and conventional raw materials. To this end, the level of contamination by heavy metals (lead, cadmium, arsenic, mercury), nitrates and nitrites, and some mycotoxins were monitored. Fifteen products were tested in their organic and conventional forms, including meat, milk, eggs, vegetables and cereals. The median levels of contamination were calculated and compared with the recommended or regulated maximum levels. The maximum levels were exceeded for lead in organic carrots and buckwheat, and in conventional wheat; for cadmium, in both organic and conventional buckwheat; for nitrates, in organic spinach; and for patulin in organic apples. Moreover, contamination of both conventional and organic wheat by deoxynivalenol was observed with a higher level in organic products. However, the health risk for consumers might be real only for the contamination by mycotoxins as the contaminated foods (apples, wheat) are the main contributors to total exposure.