Ignoring growth rates and inflation is also a huge simplification. E.g. 3% yearly growth doubles your money in about 24 years. So it may again be a factor bigger than two between the two scenarios above.
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.
Basically the thought is that 20-25 years of living expenses will generate enough income for you to early retire on.
If you make 100k (post tax) with a 20% savings rate, you save 20k, and have living expenses of 80k. Ignoring future compound growth, for each year you work, you save 1/4 a year of living expenses.
If you go the other extreme, and have 66% savings rate, you save 66k, and have living expenses of 33k. With 33k living expenses you need 660k to retire. Each year of working you end up with 2 years of living expenses. Even ignoring the effect of investment growth before you retire, that is only 10 years of working.
Of course 20 years of savings maybe be too optimistic. The book is good and has more details.