A 'farmers' market' is a market where producers [farmers] sell their produce direct to the customer. Because this cuts out the distributor from the chain, it should mean both that the food is fresher, as it has not been kept in storage for as long, and cheaper. In practice, they tend to be more expensive than supermarkets, which have the benefit of mass purchasing from suppliers, which forces down the cost of the product at source.
Farmers' markets have been particularly successful in the organic produce sector, where the customer is willing to pay a premium price for products which are free of additives: chemical treatments, fertilisers, preservatives, antibiotics, growth enhancers, etc.