Although this post is a bit more specific, most of the main reasons exercise is beneficial to teens is also true with any other age groups that may want to exercise.

Specifically for teens it may help a lot of teens focus on a certain goal and maintain that goal until they accomplish it. Often times teenagers have problems focusing or committing to a certain task, they may lose focus or lose interest quick by having a short attention span. Working out your own body will help establish a way to focus on tasks even outside of exercise, like for school or work.

Another thing that may seem obvious is that if you start exercising young, it has exponential benefits to your older self, because as you get older it becomes harder to do most exercises just with general body age and your body heals slower. So getting all of the exercises done early is a great way to make sure you stay healthy much into your older years. 

Speaking of helping out your older self, diseases often attack people with weak immune systems which is another factor of old age where you have bodily systems that are slowing down. Exercise helps the immune system remain stronger for longer as it just keeps your body in a better healthy form.