How does the system of checks and balances strengthen democracy in the United States?

By the goverment and its people

Each branch of government controls a certain aspect of the other.

Legislative can restrict the policies of the executive and judicial.

Judicial can strike down legislation deemed unconstitutional, and undo executive decisions through rulings on their constitutionality.

Executive Orders can bypass legislative channels for more efficient decision making, and can nominate if not alter the Supreme Court along with taking part in it's processes. (Some of this is my own interpretation.)