I think the idea is that if you have a large pile of money and take out a small portion of it each year to live on, due to growth the money will last indefinitely.

So if you have 25 years of living expenses and each year take out 1 year of living expenses, that is 4% of your money. If you earn ~4% a year then your account balance stays the same.

The 4% number matches the 4% rule: http://www.investopedia.com/terms/f/four-percent-rule.asp

Of course after the great recession now the common wisdom is that the 4% rule can't be trusted: http://online.wsj.com/article/SB1000142412788732416230457830...

Personally I think it would be foolish to plan on retiring with only 20 years of living expenses. However some people also plan on holding a part time job at least in early retirement.