The simplest way I've found to explain it, that everyone can follow, is this (stop after each paragraph to make sure they follow):

If you save 10% of your paycheck, after 9 years, you'll have saved a full year worth of your living expenses (because you live on 90% of your income, save 10%, so saving 10% for 9 years = 90%, the amount you live on). You can then take a year off, spend exactly the same amount of money, and then go back to work. ("Got it?" Tell them to ignore how to save that much, or the problems with the idea of getting a job when you get back, or whatever, for now, just make sure they follow the basic math of save 10% = after 9 years you can take a year off.)

If you save 20% of your income, then after 4 years, you can take a year off (because you're living on 80%, and after 4 years you've saved 20% x 4 = 80%). ("Got it?")

If you live on 50% of your income and save 50%, you can work a year, take a year off, work a year, take a year off. (At this point they go "ooohhhh" if they properly understood the earlier steps.)

If you live on 10% of your income, and save 90%, you can work a year, take 9 years off, work a year, take 9 years off. (At this point they go "wow--but no way you can live on 10% of your income," and I say maybe not, but the goal is to get as high as you can.)

Then I explain that getting to FIRE is a matter of increasing that savings rate as high as possible, and then (rather than work/time off/work/time off) doing all the work up front, so you can work a dozen years or so, then take the rest of your life off.

Then I mention that it's slightly more complicated than that, and you'll be investing the money, so you have compounding working for you (the money you invest earns more money along the way), and we get into discussions of how they think the market is like gambling, etc., but that's the basic introduction spiel I give about early retirement.

I haven't yet failed to impart the concept, even if some are skeptical of how it is done practically, they all understand the theoretical. If they want to know more about it, I link them to the shockingly simple math, and the zero to hero posts.