According to this link, there are several health benefits to playing tennis, including but not limited to:
Improved agility, flexibility, and balance. Agility is one's ability to move quickly and easily. During tennis, players usually move rapidly in several directions. Because of this, it's important to stretch before and after tennis matches.
Weight loss. Tennis is a great cardio workout. You're running, pivoting, and stretching.
Stress relief. Becuase you have to be super focued when playing tennis, your mind may stray from all the stressors that can take a toll on you. This is certainly a positive thing.
lifetime sport. Tennis can be fun for those at any age.