This item could be one that will be difficult to write; I do, however think that it is the most important. I could spend a lot of time detailing interesting recipes and helping you learn complicated techniques but it would all be a waste without a framework to put it in.
I am often chastised because I make something seem so easy to do and when someone with not as much experience tries, it doesn't come out perfect. Is this because I am such a better cook? Is it because I've tried and failed more times? I don't think so. I think it really comes down to understanding a few tenets about how food operates and therefor have a greater chance for success.
Cooking is really only about controlling two things, Temperature and Moisture.
Say you have a red hot burner and you put your hand on it. The heat that is contained in the burner is transferred into your hand and you feel hot. Conversely, if you grab a cold glass of water, the heat from your hand quickly travels into the glass and you feel cold.
Make sense? Heat works like osmosis, it travels from a place of concentration (a hot thing) to somewhere with less (a cold thing).
Seems rudimentary but here's where it get's interesting. When heat moves, it follows the exact pattern every time. It's like this. You have a full glass of water (this represents heat). You take it and pour a quarter of it into an empty glass (this represents a cold place, more aptly though a place with less heat). The water from the full glass is diminished by entering into the empty one. This is just like heat. When it travels from a place of concentration, the source then contains less heat.
Here is why this is so important to cooks.
If you are going to pan fry a steak and you drop it into a hot pan, it is going to brown but when you try and flip it and put it back in the same place it takes longer to brown. This is because much of the heat from the pan has entered the steak and it takes longer for the pan to heat back up.
A more simpler example might be making hard boiled eggs. When you drop them in the boiling water, the water cools and temporarily stops boiling because of the temperature of the eggs.
Understanding how heat works is one of the most important elements of cooking. It takes time and observation to learn it's quirks. However once you do you will be able to predict results and troubleshoot problems. Things like: "How much food can you add to a pan at one time?" or "Is this skillet too hot for these onions and will they char instead of sauté" or "Is the volume of my sauce too much for this pot and the bottom is burning while the top is lukewarm?"
Pondering these things while you cook will help you to get a more realistic understanding about this physical property. For more info on it, research the principle "the conservation of heat."
The other fundamental of cooking is learning how to control the flow of moisture in a dish. It works hand in hand with the property of the conservation of heat because temperature change immediately effects liquids. All things contain various amounts of water; from steaks to greens to mushrooms to pomegranates. It is how you control that moisture which will dictate your culinary success.
Water can be a very difficult element to control. It can have very positive or very negative effects on what you are preparing. For instance, if you are trying to cook a perfect over-easy egg you would want to drop a tablespoon of water in the pan and cover it to lightly cook the top. However, if you added a cup, the water would draw all of the heat from the pan and your eggs would be a mess. Or, if you add too much liquid when you are braising (and the meat releases it's own juices) you might boil the meat instead of braise it (shoe leather anyone?).
Observing how moisture affects cooking is not easy but in reality that and heat work together. Watching how they interact with one another is a great benefit. It could tell you why your greens didn't wilt properly or why the pancakes burned or why your chicken-fried-steak chews like a dog toy.
I would encourage anyone seeking to become a better cook to work this observation process into your food preparation ethos, you will undoubtedly hone your craft and produce higher quality food.