The province of Istanbul is one of the 81 provinces of Turkey. It is the largest province of Turkey by population (13M in Dec.2011). It has 39 districts (picture), which is lead by the governer, who is appointed by natinal cabinet, and is answerable to the Ministry of Internal Affairs. His responsibility is to execute the new laws & regulations passed by the central government. Also, the governer leads the provincial assembly, which is elected every five years. According to this article, the assembly meets irregularly and its responsibility is reduced to approving annual budgets.
At the district level, there is an elected mayor (every five year). Mayor leads the senior officials in their tasks, and is responsible for basic education, civil registration, land, posts, and telecommunications.
For the history of the local government in Istanbul and further reading: http://www.ibb.gov.tr/