Short answers, pulled from the story.
Separation of powers divides government authority into distinct branches, typically legislative, executive, and judicial, so that no single person or institution can concentrate all state power. The principle is intended to prevent tyranny, democratic backsliding, and the arbitrary exercise of authority.
The Instrument of Government, written by English general John Lambert in 1653, was one of the first documents to formally propose a tripartite separation of powers. It was adopted as England's constitution during the Protectorate and established a Parliament, a Council of State, and a Lord Protector with checks upon one another.
In Two Treatises of Government, published in 1690, Locke distinguished legislative, executive, and federative powers. He held that legislative power was supreme because it carries law-giving authority, but argued it could not govern arbitrarily, levy taxes without consent, or transfer its authority to another body.
In The Spirit of Law, published in 1748, Montesquieu argued that legislative, executive, and judicial powers must be held by separate institutions. He based his model on the Roman Republic and the British constitutional system, and warned that combining any two of the three powers in a single body would destroy individual liberty.
Separation of powers insists on keeping governmental functions in distinct institutions; checks and balances requires those institutions to have tools to constrain each other. The two ideas developed alongside each other but are in some tension, and many constitutions, including the United States Constitution, reflect compromises between them.
Bolivia, Costa Rica, Panama, Nicaragua, and Venezuela each maintain a distinct electoral branch. Sweden recognizes four branches. The Republic of China on Taiwan uses a five-branch system designed by Sun Yat-sen, consisting of the Executive Yuan, Legislative Yuan, Judicial Yuan, Control Yuan, and Examination Yuan.