Now to go into a little more depth, the idea behind the Low Carb diet craze is that carbohydrates are necessary for the STORAGE of fat - so by cutting out carbohydrates, excess energy or not, you're unable to store the fat.
Carbohydrates do help you store fat, but they're an extremely important energy source, and the only source of energy for the brain. Low carbs = low brain activity = more low carb dieters
More or less, but remember, calories aren't bad - in fact, they're not really anything. They're a measurement of the amount of energy you can get from a nutrient. You get energy from nutrients by breaking them down. The process of breaking them down results in net energy production. Once they're broken down, the individual components can be used however, but the energy is used. This is what it means to "burn calories" - it simply means breaking down nutrients and using the energy.
When you have TOO MANY energy producing nutrients in your body, your body stores them for later use. This is how bears prepare for hibernation - by eating a ton of food before they hibernate, they're able to store energy internally for the rest of winter. Unfortunately, while some stored fat is healthy, way too much stored fat is obviously a big problem.
Fat is only one of the energy producing nutrients, but it is an important one, as it is the "slow burn" energy nutrient - the one that is used for day-to-day/low-intensity activity, and for extended periods of cardiovascular activity. Fat burns slowly becuase it is more difficult to break down than carbohydrates, but results in greater net energy production.
Trans fat is a synthetically altered fat chain that is extremely difficult for the body to break down, dramatically increases LDL (bad) cholesterol levels, and is found in a number of processed foods and fast foods. It is manufactured so that oils (fats) stay more solid, and give products containing it a longer shelf life.
For you, it means tightly clogged arteries, and a much higher risk of heart disease.
Sugars are any simple (small molecule, easy to break down) carbohydrates. When you chain sugars, they become complex carbohydrates. By chaining them together, they break down more slowly and can be used over time like a fat.
Sugars can be good for rapid, high intensity activity - the downside being that since they're so simple, if they're not used quickly, they store as fat quickly as well. As you get older, as will all foods, your ability to process sugars lessens, and this becomes more of a problem. When you're a kid, on the other hand, your metabolism is so fast that you can utilize quite a bit of sugar - resulting in hyperactivity.
When eating foods, it's best to get ones that are low in sugar as these are most likely to be stored as fat rapidly.