Here's a basic example of compounding. Suppose you start with $1,000, and you earn a 7% compounded annual grown rate, over 10 years. That will grow to $1,967. See this calculator:

http://www.moneychimp.com/calculator/compound_interest_calculator.htmFor example, look at it this way:

After year 1, you earn $70, so now you have $1,070.

Year 2, you earn $74.90, so now you have $1,225.04.

Year 3, you earn $80.14, so now you have $1,310.

Year 4 you earn $85.75 leaving you a balance of $1,310.79.

Year 5 you earn $91.75 leaving you a balance of $1,402.55.

Year 6 you earn $98.17 leaving you a balance of $1,500.73.

Year 7 you earn $105.05 leaving you a balance of $1,605.78.

Year 8 you earn $112.40 leaving you a balance of $1,718.18.

Year 9 you earn $120.27 leaving you a balance of $1,838.45.

Year 10 you earn $128.69 leaving you a balance of $1,967.15.

Etc. etc.

Pretty neat math, huh?

This example, incidentally, illustrates the "Rule of 72" (

http://en.wikipedia.org/wiki/Rule_of_72) which says that if you divide 72 by your interest rate (7%), that's the number of years it takes to double your money. 72/7 = ~10 -- and in the ten years of this example, you almost doubled your money.

[Note that this is a rough way of calculating compounding but it's close enough.]

That's compounding.

By the way, the reason people emphasize so much to fill your IRAs and 401(k) is because in a taxable account, you wind up paying taxes every year on dividends (earnings the stocks produce) and on turnover of stocks in the account when the fund buys and sells stocks. That's a drag on your return. Moreover, when you ultimately sell the stock, you pay a capital gains tax on the amount the stock rose.

You ask, why is the money in your bank not doing this? Probably because you're earning only a 0.5% rate or less. Given that same number, in 10 years you will have: $1,051.14. That $50 you earned over TEN YEARS is enough to go out to a nice but not too fancy dinner. Except -- wait a minute -- in ten years, after inflation, $50 might only get you a couple of burritos and 1 or 2 beers each.

The difference in a 7% and a 0.5% return is, as you can see, staggering. This is why if you want some reward (7%), then you have to take some risk (invest in stocks, not sit in cash).

Where can you get that 7%? Invest in a total market stock fund like Vanguard Total Stock Market Index Fund (VTSMX) and Vanguard Total International Stock Market Index Fund (VGTSX). Maybe 70% in US and 30% in international. Be sure you also hold some assets in fixed income (bonds, cash) to balance the risk you're taking in stocks.

This also illustrates how MMM keeps writing about how he has "an army" of dollars working for him -- it's his investments that keep earning money by compounding, where the new money makes money, which makes more money, etc. Looking at the example above, if you had earned just $70 every year, which is the interest you earned in just the first year, then you'd have an extra $700, for a final return of $1,700. But your final return was actually $1,967 -- you got an extra $267 because of the compounding -- the earnings of the interest that you re-invested.

By the way, while it's true that the stock market has earned a high amount over very long periods of time, most experts are now tempering those estimates and expecting more like 4% to 6% (source:

http://www.bogleheads.org/wiki/Historical_and_expected_returns). These are "real" returns, i.e. inflation adjusted. For example, if stocks returned 8% "nominal" (absolute dollars) over a period of time, but inflation pulled that back by 3%, then your "real" return is 5%. Usually these numbers are expressed in real returns since that's more relevant for planning and forecasting.