Exercising for health and fitness is essential for virtually every human alive —it shouldn't be considered optional. Training for a sport is an option for those who wish to push their limits, compete against others, and strive to be the best. Logically, when you train for a sport you become very fit in the process. The discipline and dedication to training required to become competitive in a sport typically results in a lean, fit body as a secondary benefit.
However, it's important to understand that fitness training and sports performance training are very different. Failure to understand this can result in very unfortunate consequences! There is a reason why sports teams have athletic trainers and team physicians. While sports performance training definitely takes injury prevention into consideration (or at least it should), its primary purpose is to push the athlete to his/her maximal level of peak performance.
While fitness training focuses on implementing activities which are beneficial for the general health, fitness, and well-being of the body; sports performance training does not. Our culture is currently experiencing a period in which extreme training is popular — Spartan and Tough Mudder competitions, CrossFit competitions, ultramarathons, etc. These events are inspirational, motivational, and can be a lot of fun! Just remember, however, that anytime you cross the line from fitness to sport the game changes. Anything can happen, and it will, so be smart with your exercise and when in doubt, seek the help of a trainer!