Separation of powers and checks and balances are two related, though somewhat different, aspects of the US system of government. They are among the most important things in the Constitution because they are meant to protect us from government tyranny.
The Constitution implements the separation of powers by setting up three branches of government that each have their own duties and their own place in the system. We do not have a system like that of England in which the legislative branch also controls the executive branch. Instead, we have a president who is elected separately from the Congress. We have a judicial branch that is independent of the other two branches. This is the separation of powers.
But the separation is not complete. There are also checks and balances so that each branch can help to control the others. For example, the president can veto laws that Congress has passed. The judicial branch can overturn laws or executive actions if they are unconstitutional. The Congress has the power of the purse to help check both the executive and the judiciary. This is how checks and balances are implemented.