Separation of powers is the idea that no one branch of government will have control or complete power. It runs counter to the classic political notions of oligarchies and dictatorships. Separation of powers is a concept inherent to modern governments, and characteristically absent from classical dysfunctional governments. An example of separation of government is the three main branches of US govt, the Executive branch, Judicial branch, and Legislative branch. By ensuring that the powers to execute laws and enact policies and ultimately change the socioeconomic and political climate of the US are divided such that cooperation is required by three separate entities, the American people are protected by tyranny or any ill goals of a few people. Under a separation of powers, it is harder to pass into acceptance a policy or law. It requires the collaboration of all three branches. By doing so, this ensures that a government is able to only pass motions that are democratically agreed upon, and ensures that motions that are democratically unfavored do not pass.
Checks and balances are essentially the idea that one part of government over views the actions of another and ensures that no one branch is overstepping its boundaries. An example can be the passing of a law and the presidents ability to veto, for instance. Another example can be the House of Reps calling for the impeachment of the President. Such actions, highlight the ability of various parties in government to ensure that other parties act in the favor of the American people. Other examples of check and balances can include the cooperation of Congress and the House of Reps to pass legislation. In recent years, this has been a great cause of turmoil in the US sociopolitical sphere as many laws have gone un-passed, and the current Congress has gained notoriety for "doing nothing".
Overall, both of these are essential parts of government and help ensure the desires of the governed are heard and their rights, freedoms, and best interests are preserved.