"Pastured" is more commonly used to refer to poultry and their eggs, but pastured pork is out there, too. Importantly, "pastured" doesn't have a legal meaning or certification process, so the information here is more about common practices than legalities.
Pastured Pork: How It's Raised
Pastured pork comes from pigs that live, more or less, how pigs might live if left to their own devices: in fields and woods, free to move around, with small shelters where they can sleep in small groups and give birth and feed their piglets; sows are allowed to give birth in these shelters and feed their piglets.
Pastured pigs receive feed alongside the food they root for themselves. This feed may or may not be certified organic, so the pork the results from pigs raised on pasture may or may not be certified organic.
Since they aren't crowded together in unhealthy conditions, pastured pigs wouldn't commonly receive unnecessary antibiotics.
Where to Buy Pastured Pork
Pastured animals tend to be raised on small farms and the farmers often sell at farmers markets and other direct-to-consumer methods. It is usually easy to find out more about a specific farm that sells pastured meat since they are often rightfully proud of how they care for their animals and happy to share the details. Some farms raising pigs this way will even offer farm visits. Beware: pigs are smart, social animals. I don't mean to be a bummer (and I remain an omnivore), but spending much time with pigs may make you rethink whether or not you want to be eating them!
Why Bother With Pastured Pork?
People turn to pastured or grass-fed meats for a wide range of reasons. First off, the meat often has deeper, richer, or more complex flavor than factory-farmed meat does. Second, for many people, knowing that the animals they eat were raised humanely is important, as is the lessened use of antibiotics.
Finally, pastured and grass-fed animals tend to have less environmentally negative impact.
Connection Between Pastured Pork and Heritage Hog Breeds
Quite a bit goes into raising pastured pork. More than just letting some pigs run free in a field. As recounted in The Accidental Farmers, industrialized pork farms have bred out many behaviors pigs need to survive in more natural conditions, including caring for their young (sows without the right instincts will roll over on and kill their own piglets, or even trample them underfoot).
To counteract these bred-out behaviors, a lot of pastured pork comes from heirloom hog breeds, which retain instincts that allow them to live healthfully in a more natural environment. That they tend to have great flavor doesn't hurt their cause, either.