The answer that your instructor is probably looking for is that checks and balances maintain separation of powers between the legislative branch (Congress), the judicial branch (headed by the Supreme Court), and the executive branch (headed by the President). However, it is not really correct to say that checks and balances maintain separation of powers. Checks and balances actually erode the separation of powers by giving each branch some ability to interfere in the other branches’ main areas of power. Checks and balances are really meant to maintain a balance of power, not a separation of power.
Each branch of government is supposed to have its own set of powers that are separate from the other branches’ sets. The legislative branch is supposed to make laws, the executive is supposed to enforce them, and the judicial is supposed to interpret them. This is the classic idea of separation of powers.
But the Founding Fathers wanted to make sure that no one branch of government could get to be too strong so it gave each branch the ability to interfere in the others’ powers. For example, the president gets to appoint judges and Supreme Court justices, thus influencing how the judicial branch interprets laws. The president also has the power to veto laws passed by Congress, thus giving him (or someday her) some amount of legislative power. Because presidents have these powers, they can act in some ways to make sure the other branches of government do not step outside the rightful bounds of their powers. The point of checks and balances is to make it harder for any branch of government to abuse its power, not to maintain separation of powers.
However, given that your instructor has asked the question in this way, the best answer is to say that checks and balances help to maintain the separation of powers between the judicial, the executive, and the legislative branches of the government.