Best Answer: What "the rule of law" means varies by context and jurisdiction, but it's most important application is the principle that governmental authority is legitimately exercised only in accordance with written, publicly disclosed laws adopted and enforced in accordance with due process. In modern western terms, the hallmarks of adherence to the rule of law include a clear separation of powers, legal certainty, and the principle of equality before the law.
The rule of law is fundamental to a democracy, because in order for a democracy to exist, each citizen must be equal. And without it, the government is free to pass or repeal laws on their whim, and pick and choose how to apply those laws.