In addition to the usual grocery stores and supermarkets, Moscow and St. Petersburg have a large number of рынки farmers' markets. These are usually open-air affairs, though there are those which are located in large, enclosed buildings and can operate year-round. These markets are where individuals can sell the produce from their own "kitchen gardens". Here you will also find fresh flowers, a broad assortment of handmade items, such as wooden toys, knitted scarves and hats and all sorts of other things.
In the Soviet period these markets were often the only places where you would consistently find good quality фрукты fruits, овощи vegetables and мясо meat. Of course then, when the markets were the only legal havens of capitalism, the prices were much higher than they would have been in the state-owned stores. Today the markets face competition from the great number of foreign-owned stores and you'll find the market prices more or less in the line with prices in those stores.
Besides being a good source of fresh produce, the markets also provide valuable "cultural experiences". A trip to the market can be fun and interesting. But while there, you'll need to keep a close eye on your purse and wallet as these markets are the favorite haunts of pickpockets.