Some schools call it development, while others might call it advancement. The essential function of those departments is fundraising.
Private schools are run as businesses in the sense that they need to have more income than expenses in order to stay afloat. More often than not, tuitions alone are not enough to cover the salaries and capital expenditures of the schools, in which cases the schools would have to depend on donations. Children/grandchildren of major donors are usually considered development cases and evaluated separately, hence the term “development hook” or “development preference.”