Food grown on an organic farm is just as safe and healthy as food grown on non-organic farms. Organic farms do some things differently and need special certification that allow them to sell their products as organic.
An organic farmer uses organic fertilizers and pesticides, but not man-made products. The livestock are not given any growth hormones. If an animal on an organic farm gets sick, the farmers do give them medications. However, if an animal receives medication the farmer is not allowed to sell it as organic.
Organic farmers can use pesticides, but only if they are naturally occurring ones.