Metabolism is really just a measure of how efficiently your body runs. All the fancy scientific mumbo jumbo aside, what you're thinking about is why dieting works or doesn't work, or why you can or cannot gain weight.
Everyone's body is a little bit different. Some of us put on muscle easily, while others can't seem to squeeze that bicep tight enough to form any visible bump. There are many different reasons for this, one being hormone levels. Ladies: do you ever notice how you tend to put on a little weight while you're on your period, only to lose whatever was gained instantly following?
When your body is working efficiently, it is using up all the fuel that you put in each day. Your body requires energy to carry out all the normal everyday tasks. When you diet, you are asking your body to use more fuel than you give it. That causes your body to use up some of the reserves it was saving for those times when you might have to go a few extra hours between meals. Your body doesn't like this one little bit. Metaphorically speaking, if you have managed to save a little money in your bank account for a rainy day, aren't you really hoping that there are no rainy days? When this happens, your body does not want to make withdrawals from its deposits. What it would rather do is balance things back down to efficiency. There are some easy ways to do this, and one of it's favorite ways is to digest your muscle. Since muscles require lots of energy, diminishing your muscle mass will also make your body run more efficiently. TA DA! Metabolism has been lowered.
People who claim to have very high metabolic rates claim that they can eat whatever they want and not gain an ounce. All it really means is that their bodies are running very efficiently, and they are using all of the energy that they put into their bodies everyday. Of course, there are limits, and no one can really eat anything without gaining weight unless there is a medical issue. Most people who fall into this category are more balanced than they realize. They eat several small meals throughout the day, and therefore appear to be eating constantly while not consuming any more than someone eating three squares a day. They also tend to be very active - perhaps hyperactive and a little bit fidgety.
In order to increase your metabolism, you must find a way to decrease your body's efficiency. It sounds slightly counterintuitive, but it is in effect what you want to do. This cannot be done with dieting, but may be accompanied by a change in diet. What I mean is that you can't decrease calories for a short period of time, since that decreases your metabolism. You may only make a lifelong dietary change. Eating several small meals throughout the day balances the blood sugar, and makes more of the calories you take in available to your body. It also helps to increase activity and muscle mass. These are the only long term solutions which don't require medical intervention.