The phenomenon of a balloon rocket taking off can be explained by Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
In the case of a balloon rocket, when the air inside the balloon is released, it pushes out in one direction (the action), and as a result, the balloon is propelled in the opposite direction (the reaction). This principle is what allows the balloon to move forward as the air escapes from it.