To start with, running increases the anaerobic capacity of your lungs. That is, you can breathe in more air each time you inhale. THis makes your heart stronger and also increases the flow of oxygen though your bloodstream, helping flush harmful unwanted bacteria, and chemicals out of your system.
Running also helps you burn fat. The thing to remember, though, is that the faster you run, the more carbohydrates you burn. To take off the fat, you need to run more slowly and for a longer period of time. Your body should be able to sustain a longer run if it's a slower run.