To Broil means to cook food, typically in an oven, and baking with dry heat. Almost all ovens should have a broil function which means the top element is on throughout most or all of the cooking time.
The recipe will usually specify the distance that the rack should be from the element. If you need to, grab a ruler to make sure that the distance is appropriate.
Braising means to place a protein (usually a less tender cut of meat) in a liquid in a tightly covered pan. Braising can be done in the oven, on the grill or on the stove top.
To butterfly means to split food, most commonly Pork Chops or Shrimp. When the cut is made to split the food it is typically done lengthwise and not cutting all the way through.
Once the cut is made both sides can be separated and laid out flat to resemble a butterfly.
Breading is usually done to Meat or Vegetables before cooking. Most commonly breading is just that, bread. Bread can be dried or used moist depending on the recipe.
Bread is crumbled into very small pieces and the meat/vegetable is typically coated in a liquid and then rolled in the crumbled breading. The liquid will help the breading to stick better. The breaded item can then be cooked according to recipe. When it is done it adds a bit of texture and flavor to the item cooked.