The International Federation for Organic Agriculture Movements (IFOAM) defines organic farming as:
"Organic agriculture is a production system that sustains the health of soils, ecosystmens and people. It relies on ecological processes, biodiversity and cycles adapted to local conditions, rather than the use of inputs with adverse effects. Organic agriculture combines tradition, innovation and science to benefit the shared environment and promote fair relationships and a good quality of life for all involved..."
I would say organic farming is to eradicate all commercially produced synthetic pestisides and fertilizers as being used by conventional farmers.
Organic grown foods are in general (although not scientifically proven) healthier and tastier foods. The reason being, no pestisides or synthetic fertilizers are used to grow crops, therefore no adverse chemicals can contaminate your food. It has been proven that over a short period organic farming produce higher yields than conventional grown crops (depending on farmers' input).