Of course some poeple are concerned only with physical appearance when they worry about belly fat. But I think the most important reason is that abdominal fat is more dangerous to your health than other types of body fat. Having too much abdominal fat is associated with a much higher risk of diseases like heart disease, strokes, dementia, and certain cancers.
When you have a lot of belly fat, it's often a sign that you probably have intra-abdominal, or visceral fat--fat that literally wraps itself around your visceral organs, like your heart and liver. Visceral fat plays a role in inflammation inside the body. Visceral fat producec chemicals that cause this inflammation. Inflammation is extremely harmful to your body--actually, almost every chronic disease that human beings can suffer from can be tied in some way to inflammation.
Plus, excess abdominal fat is linked to insulin resistance, which is the precurser to diabetes.
You can actually appear quite thin and still have a layer of visceral fat, so it isn't really about how you look, but generally speaking, if you have a lot of visible belly fat, you're going to have more visceral fat as well
That's not to say you need to have a six-pack in order to be healthy. Of course not. But anyone who has a lot of fat stored in their abdominal region is at greater risk for a lot of health problems.
One of the best ways to fight excess abdominal fat is a form of cardiovascular exercise called interval training. Basically, instead of working at one flat pace for the entire workout you, you would do brief periods of maximum effort alternated with easier periods at a recovery pace. Weight lifting, too, helps your metabolism to burn ab fat.
Remember, though, you can't spot train your abs or any other area of the body. Doing a lot of ab exercises will strengthen the muscles underneath the fat, but it won't burn the fat away.
Dieting can help you lose fat all over, but one study by the University of Alabama Binghamton found that when they compared a group of dieters who lifted weights with a group of dieters who did not, the lifters lost more fat from their abs then the non-lifters. So the best way to lose ab fat is to eat healthy AND exercise.