FIRE stands for Financial Independence, Retire Early. The more useful half of the concept is the first: financial independence is a state, meaning your assets cover your costs, and early retirement is only one of the things you can do with it.
The arithmetic is surprisingly simple and fairly brutal: what determines time to independence is not your salary but your savings rate. Someone saving 10% needs decades; someone saving 50% needs a little over fifteen years, because every unit saved raises the numerator and lowers the denominator at once.
The movement's most common mistake is not mathematical but about purpose: optimizing for fifteen years to reach a destination without having decided what happens there. Financial independence buys options, not meaning.