For additional meanings of "Constitution (law)", please see Constitution (law).
A constitution was a series of principles for running a country or organization.
The United States of America and the United Federation of Planets both had constitutions; the United States Constitution and the Constitution of the United Federation of Planets respectively.
A council on Ventax II drew up a constitution which was later ratified by the population of the planet. Acost Jared testified to this in 2367 in a hearing to decide whether Ardra's contract would be held up. (TNG: "Devil's Due")