The concept of the new rich was coined by David Moore's book, and also explained by Tim Ferris in The 4-hour Work Week, as a response to the way many people configure their lives nowadays. The term defines a new kind of person—one that has enough money to do what she planned to do, but no more than necessary.
It also means that the person has built some kind of framework around her life in order to keep things going. Just the amount needed in case things go wrong.
This person knows that life is to be enjoyed today—not tomorrow—and believes in money as a mean of being able to achieve things today, as-we-go, and not to lie in a tomb whenever we die with gold, useless belongings, and other stuff accumulated over the years.
Of course, living today is risky; the “amount needed” to be out of danger will never be clear; and the safe zone is a comfortable one. But it seems it is worth it, because, who can assure you will be able to enjoy tomorrow?