Google and Websters are a wonderful thing:
Metabolism: The chemical processes occurring within a living cell or organism that are necessary for the maintenance of life. In metabolism some substances are broken down to yield energy for vital processes while other substances, necessary for life, are synthesized.
More muscle mass: requires more energy to sustain: increases metabolism.
Running itself increases metabolism during the activity, BUT also AFTER the activity for some time. Running and working out in general damages muscle tissue and in general moves the body's processes away from homeostasis. Over the course of the day the body needs to repair tissue and return the body to homeostasis. Because people who workout are always screwing with the system the body must have a high metabolism to keep up with it.
Now, there are people who naturally have a high or low metabolism due partly to the natural lack or abundance of muscle tissue or other reasons.
Heart rate relates to metabolism when it departs from resting value. Increased heartrate means increased workload and that requires a higher metabolism. So when you're working out and your heart rate increase calories are burned at a faster rate and metabolism is increased.
As a general rule of thumb you can calculate your BMR (Basal Metabolic Rate), which is the # of calories your body needs just for daily living (if you sat in bed all day) by multiplying your weight times 10. This is a VERY BASIC way of calculating BMR. If you want to know a more detailed forumula look it up. You can usually assume another 500 calories for daily activities. So...lets take me...140 lbs...1400 BMR, 1900 total if I did no exercise at all. So, you can see how easy it would be for someone who didn't exercise to gain weight. Add 1000-2000 (10-20 miles) to the 1900 for my daily running and you have 2900-3900 calories a day.
Now, if you take in more calories than you burn you'll gain weight. If you expend more calories than you take in you'll lose weight. Many people can't seem to grasp this simple concept. You can exercise and eat well all you want and not lose weight unless you create a calorie deficit. You could eat nothing but twinkies all day and lose weight if you want you take in is less than what you expend. This is why Atkins worked for some...it's a low calorie diet in disguise.
Alan