Yoga involves many components, the asana or poses is the one strand that most of us are familiar with in the West.
The components that are beneficial to children and young adults include the focus on mindfulness - essentially the ability to be in the moment, aware of of your perceptions, external environment and thoughts, but able to pause prior to reacting; and the development of the awareness of your own body and those around you in space, which is a developmental pre-cursor to social skill development.
The brain evolved from the brain-stem up and forward - with the complex frontal lobes being the last to develop. The awareness of your own body and others in space is the evolutionary basis for social intelligence - that is, your ability to recognize the emotional expression on your friend's face, for example, requires the harnessing of the areas of your brain, which tell you that your left foot is to the left of your right foot, in space, when you are standing on the subway. Learning where your body is in space and how to make complex and subtle adjustments to your physical body is a key feature of the asana practice of yoga.
Mindfulness is developed through meditation practices and the focus on the breath and self-inquiry during the asana or poses. I consider mindfulness to consist of the ability to "put on the brakes" - essentially learning how to pause before reacting to either external stimuli or internal thoughts/desires/intentions.
Yoga involves in-depth learning of where your body is in space and how to isolate and move very specific parts of your body in relation to other parts of your body. This practice develops those areas of the brain that are key to the development of social intelligence.