The Nawabs of Bengal were the hereditary nazims or subadars (provincial governors) of the subah

Subah

A Subah was a province of the Mughal Empire in South Asia. The governor of a subah was known as a subahdar, which later became subedar to refer to an officer in the Indian Army...

(province) of Bengal

Bengal

Bengal is a historical and geographical region in the northeast region of the Indian Subcontinent at the apex of the Bay of Bengal. Today, it is mainly divided between the sovereign land of People's Republic of Bangladesh and the Indian state of West Bengal, although some regions of the previous...

 during the Mughal rule

Mughal Empire

The Mughal Empire ,‎ or Mogul Empire in traditional English usage, was an imperial power from the Indian Subcontinent. The Mughal emperors were descendants of the Timurids...

 and the de-facto rulers of the province.
From 1717 until 1880, three successive Islamic dynasties — the Nasiri, Afshar and Najafi — ruled Bengal:

The first dynasty, the Nasiri, ruled from 1717 until 1740. The founder of the Nasiri, Murshid Quli Jafar Khan, was born a poor Deccani Oriya Brahmin

Brahmin

Brahmin Brahman, Brahma and Brahmin.Brahman, Brahmin and Brahma have different meanings. Brahman refers to the Supreme Self...

 before being sold into slavery and bought by one Haji Shafi Isfahani, a Persian

Persian people

The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...

 merchant from Isfahan who converted him to Islam.