
The reason is very simple: to burn the extra calories he gets from food and the sugar-sweetened beverages and to help him develop physical and mentally. Exercises keep everybody in good health, they always improve kids health and further development in life.
There are a few main types of training for a human being, depending not only about the muscles involved, but the target: cardio training (as wind sprints, hill sprints, burpees, stair climbs and mountain climbers, dynamic jumping), core bodyweigh training (as pullups, pushups, dips, situps, squats and lunges), endurance training (as running and swimming), strenght training and agility (basic gymnastic or acrobatic moves).
Of course, when children are involved only a small part of training should be done. Everybody should be capable to run, swim and ride a bike for some distance, but a man should start developing his/her big muscles only after puberty. When childhood the most important things is to works on all muscle strengthening and swimming is perfect for that. Basic aerobic exercises are great for strengthening the muscles and the bones, along with the stretches done during warming-up.
Exercises for kids depends in some manner of their age and personality: girls might love more dancing or playing tennis, boys might enjoy better playing football (soccer), basketball or hiking (more than just climbing the trees). So you should try combination of exercises in order to see wich of them are fit to your child. For example, everybody may love rollerblading from time to time.
Consider that team sports will make the children act together in order to accomplish a goal. This is essential for their further development as human beings living in one big community. All the sports, but the martial arts in special, help building the respect and appreciation about oneself and others.
During the history some children (the Mongol tribes are well known for that) learned to ride a horse before learning to walk, but that age is far too small to make a child to exercise. Swimming is the first sport to start with, and later, when the kid is about 5 or 6 years of age you can introduce him (or her) with other sports.