Financial Independence means having enough saved up so you don't need to work anymore. A good estimate is 25x your annual spending. Once saved, you can withdraw 4% annually from your portfolio to cover living expenses. This total may be lower if you have another reliable source of income (eg real estate properties or a profitable side project).
FIRE is an acronym for Financial Independence & Retiring Early. It's important to separate the two, because being financially independent does not force early retirement. Reaching FI gives you freedom to: start your own business, work part-time, pursue hobbies/charities, spend more time with family, travel full-time, or retire early. FIRE is achieved by aggressively increasing your savings rate — via increasing income and/or decreasing expenses.
LeanFIRE vs FatFIRE
Two strategies came out of the original FIRE community:
LeanFIRE pursuers have a more minimalist/frugal approach. Usually their annual spending is below $40k/year, which puts their FIRE number below $1M saved. For a software engineer, this may mean saving aggressively during the initial stages of your career — before retiring early.
FatFIRE pursuers hope to accumulate a large amount of wealth. There's no specific threshold, but having an annual budget of above $200k/year would put their FIRE number above $5M saved. This may mean staying employed in your career longer to take advantage of later, high-earning years as a senior individual contributor or manager.