The Harvard Number is the amount of money Harvard would want as a donation for accepting your kid as an undergraduate. It's not the kind of information they post on their website. You have to ask the right people in the right manner.
He said he just found out that the current Harvard Number — assuming your kid's application was "competitive" (i.e., there's some chance your kid would get in even if you didn't write a check) — is $5 million.
If your kid's "not competitive," then it is $10 million.
If there are about 1,800 freshmen at Harvard each year, then Harvard could admit, say, 100 competitive applicants whose fathers (typically, hedge fund guys) write the Harvard Number on a check — without tangibly lowering the quality of the class. That's, theoretically, a half billion per year in virtually free money. How could an institution resist that temptation?
Quid pro quo arrangements aren't supposed to be tax deductible as charity, but how often does the IRS get the goods on this? In practice, a big chunk of the Harvard Number gets refunded by the taxpayers.