What is the system of check and balances?
The system of Checks and Balances comes about from the idea of not allowing one power to become more powerful than other powers. For example, the U.S. Constitution implemented a system of checks and balances by establishing three branches of the government, each answerable to the others in their own way. The Executive Branch controls much of the government's operation, Congress passes laws, and the Judicial Branch rules based upon the law. But the Executive Branch passes a budget to Congress to approve for its operations, which they are not obligated to pass as-is; while Congress creates and passes laws, the Judicial Branch (the Supreme Court) can rule whether the law passed is constitutional or not or define what scope the law pertains. If Congress doesn't like the way the Supreme Court ruled on a law, they can change the law, which brings it back under the jurisdiction of the Supreme Court if it is challenged. Likewise, the Executive Branch has the ability to veto a bill that Congress has passed to become law. And the Supreme Court constantly rules in cases that have been brought against Departments within the Executive Branch. Like I said, the idea is that no one branch of the government can become despotic because the other ones are able to limit its power before that point.
Why did the framers of the constitution include a system of checks and balances in the Constitution?
The purpose of the checks and balances system is to ensure that one arm of the government system does not hold too much power. Each branch will have the power to check whatever the other branch is doing. Without this kind of system, one branch will become too powerful thereby rendering the other powerless.