The separation of powers and checks and balances are very important in giving power to both the federal government and the state governments, along with balancing power within the branches of government. Balancing the power of both the federal government and the state governments has always been a prominent issue in history, in some cases even splitting the country apart.
The separation of powers is essentially what it sounds like, separating the powers between the federal government and the states. Both have power and the people maintain the power to essentially overthrow and change the government if the government does things that are not in the best interest of the people and the country. While the federal government holds the most important powers, any powers that are not designated for the federal government goes to the states.
The checks and balances are important as well, as this prevents certain branches of government from obtaining too much power. The branches of government all hold key powers, all of them being balanced and can check each other if one has too much power.