It comes from the 1998 Trinity study, which tested stock-and-bond portfolios against US market history and found that a 4% initial withdrawal, inflation-adjusted each year, survived thirty years in the large majority of periods examined.
Its real usefulness is as a sizing rule: inverted, it says you need roughly 25 times your annual spending. That is the number which turns "I want to be independent" into a concrete figure, and it is why the rule became famous.
Its limits matter just as much: it assumes thirty years (not fifty), twentieth-century US markets, spending that never adjusts downward, and zero fees. With 1% costs, longer horizons, or high starting valuations, the safe percentage is lower. It is not a law of physics: it is a starting point for running your own numbers.