Maximum heartrate is pretty much set by genetics and decreases with age. The most common estimate for adults is 220-age=max heartrate. So the average 20 year old would have a max heartrate of 200 bpm. This formula, although widely used, is not very accurate. The only way to know your max heartrate is to test for it. However, increased fitness does not increase the maximum heartrate - at least not significantly.
With improved fitness, an individual should see a reduction in the minimum (or resting) heartrate and an increase in the anerobic threshold heart rates and lactic acid threshold heart rates.