It is located inside a building that, due to a magic spell, it's bigger on the inside than on the outside.
Kamar-Taj is the place where the Masters of the Mystic Arts live. There, they hone and focus their magic powers, and after they've mastered it, they use it to protect the world from the forces of evil.
Due to their connection to Kamar-Taj, the Masters of the Mystic Arts are better known as the "Masters of Kamar Taj".
Stephen Strange moved there to find a cure for his disfigured hands. While his hands eventually did heal, the important thing is that he learned magic there, himself becoming a Master of the Mystic Arts.
The rightful ruler of Kamar Taj is the Sorcerer Supreme, the most powerful Master of the Mystic Arts in existence. The Ancient One used to be the Sorceress Supreme, but now that she's dead, Stephen Strange is the next in line to become the Sorcerer Supreme.