The Court of the Fountain was the courtyard that was built upon the top of the prow of Minas Tirith. The courtyard was where the house of power in Gondor lies and where the White Tree of Gondor grows. It was guarded by the Guards of the Citadel.
The court covers the flat area at the top of Minas Tirith's prow. It has several small patches of grass growing on it, with a fountain in the middle. One can walk out onto the prow from this court, and can access the bench-like seat at the end of the prow. One can also access the Citadel from the court.