Financial independence (FI) means having enough financial assets that you could live the rest of your life without working. Bloggers frequently use the FIRE acronym which stands for [become] financially independent and retire early. Such a life might be pictured as living off capital gains from one’s investments without reducing the principle, much like how a university or non-profit foundation lives off its endowment in perpetuity (albeit, often subsidized with tuition, sales, donations, etc.).
If FI means not touching the principle, this means you could live to 100 and your original investment would still be there (even when adjusting for inflation). This requires a combination of frugal living and large amounts of accumulated assets. You might be able to achieve FI with just a quarter million in assets if they live in a low-cost-of-living area, behave frugally, and invest in the stock market at-large (e.g., an S&P 500 index fund). Although there is luck involved (e.g., what the market does), one can certainly influence their income, investing, and spending. (On the other hand, if one chooses to avoid stocks entirely, it would be difficult or impossible to achieve FI with bonds or Treasury bills, due to their low propensity for growth.)