No, the Rule of 72 has nothing to do with your age, or Required Minimum Distributions (which start at age 72 and involve taking distributions from taxable retirement accounts). Long before you start taking money out of your savings, you will be deciding how much money you need to put in to save enough for a comfortable retirement. More importantly, you will probably want to know how long it may take to achieve your savings goal. That's where this rule comes in handy.
The Rule of 72 helps you to quickly estimate how long it will take for your money to double at various rates of growth. For example, if your money earns 4% annually, divide 72 by 4 (answer: 18) and that's roughly how many years it will take for your money to double. At a 10% return rate, your money would double in approximately 7.2 years.
The results from this rule are approximate, not precise, but they are, "close enough for government work", as the saying goes. The higher the return rate used, the less precise the rule is, but even at a 15% return rate, the rule is off by just a couple of months. It still works well even at a 25% return rate.
Another benefit of this rule is that it also works in reverse. If you got a late start with retirement savings, and need to save a certain amount in the next 8 years, for example, just divide 72 by 8 (answer: 9), and the result will be the rate of return you will need to accomplish that goal (9%).
There are, of course, plenty of calculators that can give you a very precise answer (down to the number of days) to these type of questions, but unless that degree of precision is necessary now you can do it yourself with very quick and simple math. One caveat - remember that this assumes a perfectly consistent rate of return for many years in a row. Any fluctuation in those returns will affect your results accordingly. Using a realistic average rate of return will offer better accuracy than using a more optimistic rate.