Braising (from the French word, “braiser”) is a combination-cooking method that uses both moist and dry heats: typically, the food is first seared at a high temperature, then finished in a covered pot at a lower temperature while sitting in some (variable) amount of liquid (which may also add flavor). Braising of meat is often referred to as pot roasting, though some authors make a distinction between the two methods, based on whether additional liquid is added.
Braising relies on heat, time, and moisture to break down the tough connective tissue (collagen) that binds together the muscle fibers collectively called meat, making it an ideal way to cook tougher, more affordable cuts. Many classic braised dishes (e.g., coq au vin) are highly evolved methods of cooking tough and otherwise unpalatable foods. Both pressure cooking and slow cooking (e.g., crockpots) are forms of braising.
Most braises follow the same basic steps. The food to be braised (meats, vegetables, mushrooms, etc.) is first pan-seared to brown its surface and enhance its flavor (through the Maillard reaction). If the food will not produce enough liquid of its own, a certain amount of cooking liquid that often includes an acidic element (e.g., tomatoes, beer, balsamic vinegar, wine) is added to the pot, often with stock. A classic braise is done with a relatively whole cut of meat, and the braising liquid will cover two-thirds of the food in the pan. Then, the dish is covered and cooked at a very low simmer, until the meat becomes so tender that it can be "cut" with just the gentlest of pressure from a fork (versus a knife). Often the cooking liquid is finished to create a sauce or gravy, as well.
To what do you not drive
Mortal hearts
Accursed hunger for gold?
Cheaply bought, but deadly sold
With new light they shine on through
On fields of shredded goals
Reap crop of clinging hope
Harvest our brave new world
Ancient woe, be gone
Foul illusions of better life
Compared to what, I ask
Does this truth of life coerce?
Juxtaposed they are not