Farm house sinks have evolved over time. The earliest farm houses did not have running water and any cabinets in the kitchen would be more like furniture than the built-ins we have today. A kitchen sink was usually placed next to a window to allow water to be poured into the sink from the outside. In America, sinks were initially made of stone or lead lined wood, copper, or ceramic, then eventually were made of enameled metal and then stainless steel.
Below is a photo from the Historic American Buildings Survey taken in 1939 of a Shaker canning sink. More of a stand alone element in the kitchen, it served them well in their task of preserving the harvest.
Modern farm sinks allow the user to be as close as possible to the sink bowl (compared to a conventional sink set into or on top of a countertop), and at the same time provides a waterproof front in case there are minor splash overs.