In America we have our 3 branches of government- Executive, Legislative, and the Judicial branch. The legislative branch is what makes our laws. It is ran by the Congress (House and Senate). It is used to create laws, declare war, and to regulate taxes.
The executive branch is ran by the President, Vice president, and the cabinet. Legislative is responsible for enforcing the laws whether is a federal law or a state law. They carry out the laws.
The Judicial branch is what applies the laws. They also go over any cases or debates about laws that are put in by the congress or constitution.
The system of checks and balances serve as a system to make sure that none of the braches of government gets more power than the others. It *balances* (pun indented) the amount of power each branch has. Checks and balances is also known as separation of powers. Which is why it's so important because it keeps the branches equal.