What made Baghdad Cairo and Cordoba important in the Muslim world?

Answer 1
Cairo has been an important capital of the earlier Muslim Province of Egypt. It has also been a famous place of learning and trade centre.

Baghdad had been the Capital of Abbasid Caliphate for many centuries. It has seen the Golden period of Islam. It had been the most important centre of culture, arts and learning.

Cordoba had been the capital city of Umayyad Caliphate for many centuries.
It had been the most important centre of culture, arts, and learning during a period when most of Europe was called wild, wild West.

Answer 2
The three cities were the capitals of the Fatimid (Cairo), Umayyad (II) (Cordoba), and Abbassid (Baghdad) Caliphates. In each were established great universities, important mosques, large markets, and huge bureaucratic centers.