On-farm processing refers to the practice of taking the crops you grow or livestock you raise and processing them into a new and different product. For example on-farm processing may mean you turn veggies into salsa, fresh fruit into jam or process milk into cheese.
The National Organic Program (NOP) notes that processing in general refers to the following practices: cooking, baking, curing, heating, canning, drying, mixing, grinding, churning, separating, extracting, slaughtering, cutting, fermenting, distilling, preserving, dehydrating, and freezing. If you do any of the above on your farm, then you're engaging in on-farm processing.
Processing also includes the repackaging of foods from bulk bins into smaller containers labeled for organic retail sale, although this is less likely to occur on the farm.
A farm that adds value-added products will, in almost all cases, also be participating in on-farm processing, although some farms do send their initial products to another facility to be processed.
Keep in mind that on-farm processing, in most cases, means you'll not only need to be certified as an organic producer but as an organic handler as well.