Calisthenics is a form of exercise that consists of gross motor skills. Gross motor skills are the physical skills required as adults to move including running, standing, grasping, pushing. If you can do all of this with grace, you would be called athletic. Done as exercise, it helps you increase your body strength, body fitness. You also build flexibility through the various movements and stretches. If you add weights to your moves, you end up creating strength.
Some of the exercises that form part of calisthenics include lunges, jumping jacks, squats, squat jumps, sit up, crunches, push-ups, and pull-ups. You may have seen the bars in the parks that people use to lift their body weight while doing pull-ups. If you have never tried these before, these are not easy to do and will tax even a moderately fit person. Remember, if you are trying these exercises, your goal is to fail to mean to keep doing the training till you cant do it anymore. Failure, in this case, means you repeat the exercise till you cant anymore.
As we moved to urban cities, with fewer spaces, people began to look at calisthenics or street workout as a form of exercise. Names after the historian Calisthenes, a Greek historian, the kind of training evolved over the ages, to also become Gymnastics. A good physical instructor would tell you to mix this form of exercise with something else. Unless you are doing this regularly and with sufficient intensity, it may not end up being adequate exercise especially since your body will adapt. You need to increase the intensity of the activity which may not occur through pure calisthenics. For those of us in urban cities, though, this beats the hell out of a moderate intensity morning walk, the benefits of which wear out very quickly.