A national university is a university created or run by the national government, most today however are autonomous from government interference. National universities are often closely associated with national cultural or political aspirations. For instance the National University of Ireland in the early days of Irish independence collected a large amount of information on the Irish language and Irish culture.
There is no national university as such in the United States, but American University is considered the nearest thing as it was set up many years after George Washington expressed a desire for an "national university".
See also
List of national universities