Minas Tirith meant 'Tower of the Guard'. It was also called the White City, and the City of Gondor. It was known as Mundburg to the Rohirrim.
Formerly Minas Anor, it was renamed Minas Tirith at about TA 2002, when the Nazgûl captured Minas Ithil.
It was the citadel of the Kings of Gondor after the destruction of Osgiliath. In the centre of the topmost circle was a tall tower called the Tower of Ecthelion. It was built by the Steward Ecthelion I in around TA 2719. The tower was used to bear the standard of the city, and for some time housed one of the palantíri. The White Tree of Gondor was planted in the Courtyard after Isildur's escape from Minas Ithil.
The Mirror of Galadriel is a silver basin that was used by Galadriel to see the future, the possible future, or to see the happenings in the distant lands. When left to its own devices, it could show anything.
Galadriel used it to show Frodo what would happen if he had failed at his Quest.
She was able to use the Mirror because she bore one of the Rings of Power, Nenya.