I think the OP might be referring to the story in David Chilton's "Wealthy Barber." Basically, it's about twin brothers. At age 20, one brother starts saving $2,000/year, while the other does nothing. 6 years later, the first brother stops saving, and never adds anything else to his IRA, while the other brother finally gets his act together and starts saving. The second brother saves the same $2,000/year, for the next 37 years. By then, they're both 65 years old, and by the magic of compound interest, they have the same amount of money, even though the first brother hasn't added another penny in the past 37 years.
The story works because it uses a rate of return of 12%.
Examples like that bug me because they rely entirely on the rate of return. In the real world, you will never ever get a consistent 12% return, year after year, for 45 years in a row. In the real world, the rate of return bounces around all over the place. Some years might be up 20%. Others might be down 35% (see 2008). Inflation exists. And if you're adding new funds along the way, then even the order of the returns matters. Specifically, if you're just lumping $1 million into an IRA on day 1, to leave it to grow for the next 30 years, the order of the returns doesn't matter. But if you're constantly adding new money every month (as most of us do), then you would rather have modest gains in the early years, with the big gains in the later years, once you've had time to get more money in there.
Beyond all that, 12% is an unrealistically high average rate of return anyway. Even 8% looks overly optimistic these days. Warren Buffet says we should aim for 7%. And that's for an all-stock portfolio. As we know, we're supposed to be shifting more and more toward fixed-income as we age, decreasing our exposure to stocks. So how are we supposed to earn even 7%, if stocks only make up 60% of our portfolio?
Though the "Twin Brothers" story makes a compelling argument about compound interest, and it certainly serves to grab the interest of young newbies who might otherwise neglect to start saving for their own future, it's grossly inaccurate. In the real world, the second brother would have far more money than the first.