What I consider to be your metabolism is your resting metabolic rate. This rate is the amount of calories that your body burns to perform basic metabolic functions. Just resting your body burns calories and in order to live your body needs fuel to function.
The release of energy at rest is sufficient only for the functioning of the vital organs, the heart, lungs, nervous system, kidneys, liver, intestine, sex organs, muscles, and skin.
Your body does not need fuel to maintain bodyfat (or very very little fuel) but it needs significantly more fuel to maintain muscle. If your metabolism is dependant on burning extra calories for the above then the only one that can increase in size is your muscle. So if you have more muscle your resting metabolic rate (i.e. metabolism) is increased because your body at rest has to expend more calories.
There are specific exercise and nutritional things that need to happen to increase lean muscle tissue but the pure fact is that your body will burn more calories at rest and require more food if you have more muscle tissue.
Muscle needs calories to function and maintain, fat does not.