Discard X after simmering- many flavorful compounds are fat or water soluble. Flavor compounds aren't infinite, and are distributed by osmosis/diffusion. In addition, some flavor enhancers aren't tasty after they been simmered. It makes sense to discard them. Examples Bay leaf, bones, cheap vegetables.
Cooking temperature- water in food boils at 212F and will not go higher until the liquid water boils off. This affects Browning/searing food.
"sugar is a liquid ingredient" - could be remembering the quote wrong but heard it on Good Eats and it makes recipes make sooooo much more sense.
Some major methods of cooking:
Roasting-cooking in dry heat, usually in an oven. Baking is basically roasting.
Deep frying-frying in enough fat to submerge the food being cooked.
Sautéing-cooking in a small amount of fat.
Boiling-cooking in a large amount of water.
Steaming-cooking in a closed vessel, with the food being cooked elevated over the liquid.
These days there is also Sous-vide cooking, where the food is sealed in a bag before being submerged in water heated to a precise temperature.
Bullion cubes- a beef bullion cubes is beef broth that has no water.
Broth- beef broth is beef fat with flavoring, and salt with water.
Searing - to brown food/meat/veggies on a hot pan, usually with fat to conduct heat faster. Purpose is to improve flavor. Downside overcooks the layer underneath the browned/seared area.
Fond - when brown bits of food get stuck to the pan instead of your food or mouth. It's tasty, 5 stars on Yelp.
Reducing-concentrating flavor by evaporating water from a liquid. If you reduce with an oven, it's possible for the liquids on the surface of a pot to evaporate enough water that it enables browning. Say the bubbly browned cheese in a potato gratin.
Edit 3/1/19 Compiled the posts into 1.