Minas Anor was the original name for Minas Tirith, the great city of Gondor. It means "Tower of the [Setting] Sun" in Quenya (from minas = "tower, citadel" and Anor = "Sun") and was built across from Minas Ithil, the "Tower of the Moon". Both were raised in the last years of the Second Age, when the Kingdom of Gondor was still young.
Originally a simple fortress, Minas Arnor was significantly expanded during the reign of King Ostoher. Starting around 420 in the Third Age, he spent a decade turning the citadel into a city, from which he took his name, which is Quenya for "Fortress Lord".
In Third Age 2002 the Witch-king of Angmar led an army from Mordor that conquered Minas Ithil and renamed the citadel Minas Morgul, "Tower of Sorcery". Gondor, now on the defensive, renamed Minas Anor as Minas Tirith, "Tower of the Guard".