The term 'grounded' no doubt comes from the action taken when the behavior or performance of an airplane pilot indicates that he or she should not be entrusted to continue flying -- at least temporarily. It is said that the pilot is 'grounded' -- i.e. must stay on the 'ground', no longer permitted to fly.
So when children 'fly too high' in their behavior, the parents take away their 'wings'. They are grounded. This usually means they cannot go out with friends, cannot go to leisure time activities outside of school (shopping, movies), etc. They go from home to school and home again. That's all.