Here is one definition:
The rule of law requires the government to exercise its power in accordance with well-established and clearly written rules, regulations, and legal principles. ...The current USA citizenship exam asks What is the "rule of law"? Our elected officials have to take an oath of office promising to obey the rule of law.
Under the rule of law, no person may be prosecuted for an act that is not punishable by law. When the government seeks to punish someone for an offense that was not deemed criminal at the time it was committed, the rule of law is violated because the government exceeds its legal authority to punish. The rule of law requires that government impose liability only insofar as the law will allow. Government exceeds its authority when a person is held to answer for an act that was legally permissible at the outset but was retroactively made illegal. This principle is reflected by the prohibition against Ex Post Facto Laws in the U.S. Constitution.
For similar reasons, the rule of law is abridged when the government attempts to punish someone for violating a vague or poorly worded law.
The rule of law requires that citizens can only be punished for offenses that are codified in writing somewhere. The family court is a modern exception.
I have been punished by having my kids taken away from me, and ordered to pay non-guideline child support. No one even claims that I have violated any written rule, or that I am an unfit parent, or anything like that. The core problem is that the family court does not respect the rule of law.
I should not have to explain why rule of law is superior to the rule of Muammar Gaddafi or King George III. It has been obvious for thousands of years. Someday everyone will agree that the family court is barbaric.