Despite being a Rockefeller, as a child Ariana Rockefeller had to record her allowance — how much she got, how much she spent and where, she said.

"The message was, a dollar is a dollar and to value that and to put a lot of value on hard work and the enjoyment of life, of course, and to give back," Rockefeller told CNBC's Robert Frank on "Power Lunch" Thursday.

In fact, her grandfather, David Rockefeller, the legendary American banker who died in 2017, gave back about $2 billion over his lifetime to various philanthropic endeavors.

This week David and Peggy Rockefeller's personal collection is on sale during a weeklong auction at Christie's in New York.

"There's a time for private life, and there's a time to step forward," Ariana Rockefeller said. "This was really my grandparents' vision."

The auction house estimated the collection to be worth about $500 million. As of Thursday, the collection had made more than $765 million, including the sale of a Picasso painting for $115 million. Proceeds from the auction will go to charity.

The collection includes the family's personal artifacts, such as a treasured picnic basket, candlesticks, paintings and fine china, among other things. Rockefeller said she is excited that the public loves the collection as much as her grandfather did.

"He really used almost every piece in his collection and loved it," she said. "I think my grandfather had such great taste, and he really cherished beautiful things."

All family members got to keep one item from the collection, worth up to $1 million, she said. Rockefeller, who launched her own fashion and apparel label in 2011, chose a bracelet her grandfather once bought for her grandmother.