The "power of the purse" is the practical as opposed to legal method by which the legislative branch checks the executive and even the judicial branches of government. Neither of those two branches can raise money or appropriate money for things they need, therefore tey are dependent on Congress. If the President wants to commit troops to fight somewhere, the President cannot do so unless Congress appropriates money to pay for the soldiers, equipment, etc. If the Supreme Court wants more members, the Chief Justice cannot add them unless Congress appropriates the money to pay for them. This power also extends to threats by Congress to the President and Judiciary to reduce appropriations for other matters (except compensation during their terms) unless they do what Congress wants. It is a powerdul tool but not absolute.