The rule of 72 is a quick rule of thumb to help you understand how quickly your money can grow.  It works like this:

Take the return of an investment, say 9% per year.  Divide 72 by 9 and you get 8.  That is the number of years it will take to double your investment.  If you make 5% a year, it'll take 14.4 years.

You can turn it around.  If you want your money to double in a decade, what return do you need?  72/10= 7.2% per year.  (Don't forget to adjust returns for inflation- that's 7.2% AFTER inflation)

You can also use the rule of 72 to understand how much something is going to cost you.  Say you buy something on a credit card that is 29% per year.  How many years will it take before you're paying twice as much as you should for the purchased item?  72/29= 2.48 years.  No wonder those guys send out so many credit card applications each year.

Math nerds- Yes, I know the rule of 72 should really be the rule of 69.3.  That's okay, it's close enough for good estimates.  You guys can go play with the Rule of 114 (time to triple your money) and the Rule of 144 (time to quadruple your money.)