A farmstead cheese is made from milk produced on a specific farm. Farmstead cheese are often made in creameries located on the farm, but always at least quite nearby, since fresh milk is perishable.
Farmstead cheeses are thus made in relatively small batches and many steps are usually done by hand (such as turning the cheese, wiping the rinds, cutting, and packaging). Because farmstead cheeses are made in a specific place, they tend to develop unique flavor profiles based on the feed the animals receive, the climate in which they're made, and the natural microbes in the air where they are aged.
Some "artisan" or "artisanal" cheeses are also farmstead cheeses, although some artisanal cheeses are made by cheesemakers who buy milk from a few farms. Some larger creameries will make farmstead cheeses (cheeses made with milk from specific farms) and other artisanal cheeses made with milk from several farms, using the same care and techniques for both.
Many farmstead cheeses are organic, but many are not. Organic cheese needs to be made with milk from animals that, along with not receiving hormones or antibiotics, which many farmstead dairies follow, have only been fed organically grown feed. Organic feed is remarkably expensive and many farmstead cheesemakers can't re-coop the cost. If organics are important to you, it should be relatively easy to find out the specific animal husbandry practices followed by any farmstead cheesemaker by looking on their website or giving them a call!