Seriously? At Stanford? Every professor other than Daphne (I believe) at the AI lab has worked for Google at some point and Stanford is the last place where CS profs look down upon starting companies.
Starting a company wasn't the issue. It's more that for-profit education has a bad reputation (think University of Phoenix). There was some initial concern/confusion.
Non-profit organizations (mostly corporations) are defined as non-profit by having no residual claimants. That means that if there is money left over after the bills have been paid, that money (roughly "profits") does not accrue to any stockholders or other interested parties but can only be used for ongoing operations.
Responsibility is usually held by a board of directors or trustees that appoints its own successors but that is not universal.
Often the managers of a non-profit will balloon their salaries or give bonuses to the board of directors if there is money left over. This is a form of corruption but remains common.
A 501(c)3 corporation in the USA is a type of non-profit that receives special privileges, the most obvious of which is that contributions can be written off the taxes of the donor. To be a 501(c)3, a non-profit corporation has to be former for one of a specific set of public charitable purposes and meet special reporting requirements. The principal purposes that qualify are churches and schools but also include aid to the poor and others.
IRS publication 557 details the rules for 501(c)3 and other tax-exempt non-profit organizations.
It's a 501(c)(3) like most private American universities. This means there are no "owners" who make money if it brings in a profit, but conversely allows it to accept tax-exempt charitable donations.
