An endowment is a sum of money that someone donated to Harvard or Stanford. Often some people will make a provision in their will to donate some of their money as an endowment to a particular university (perhaps their alma mater) or a favorite charity.
The money is put into a trust and then invested so that it can earn interest or dividends. The private equity group in your question is managing the funds for those particular trusts. (The trust usually has a board of directors that must vote on any decision to be made with the fund's assets.)