Braising is a technique used to produce well flavored, tender meat from lesser, or more tough cuts. To braise, one seasons, and browns the meat to add flavor, then adds a small amount of water, and covers with a tight-fitting lid. Cooking is done at a low temperature (between 190 and 325 usually) to slowly break down the meat proteins, and connective tissues. Water doesn't cover the meat, and so doesn't leach flavor from the meat.
Simmer is to cook at a temperature just under boiling, with the food immersed in water. Simmering does extract flavor from the foods in the liquid, resulting in broths, stocks, or gravies. Simmering is very similar to stewing. Simmered meat has less "meat" flavor than does braised meat.
Poaching is cooking by total immersion at low temperatures (170 to 190), and is usually done just long enough to bring food to a desired temperature. Foods can be poached water, or cooking oil.
Boiling meat can cause it to become tough and dry, if the meat is boiled too long. I once placed bratwurst into my slow cooker on its high setting and let it cook all day. Eating the resulting sausage was like chewing on sawdust cemented together with rubber glue.
Though cooking in bubbling oil was once called boiling in oil, it is now referred to as frying.
Moral of the tale; Know your techniques, and what they are called, and both when, and how to use them.
Seeeeeya; Chief Longwind of the North