That's a complicated question and it depends in large part on when and where in that period you're talking about. In very general terms in this period we're looking at states with a military and political elite consisting of Turkic tribal dynasties that's overseeing a settled population of Arabs and Persians. While the vast majority of these Arabs and Persians would be engaged in basic agriculture they also occupied the religious and socially elite positions. Despite often maintaining Turkic languages as the languages of court (or else using Persian) the Turkic dynasties were nonetheless Muslims, and so despite dynastic turnover the Islamic cultural, religious and legal institutions were a bastion of stability that allowed social continuity despite quite a lot of political change.

This has been referred to, since Marshall Hodgson, as the Amir-Ayan system, which might translated as the "The Generals and the Notables" system, i.e. a system of relations between the Turkic military aristocracy and Arab/Persian elites.

One of the defining features of this system was the Iqta, which wasn't really one system but actually had several distinct variations. While this has been analogized to feudalism, the peasantry were not tied to the land in a system of serfdom and the granting of an iqta did not incur an obligation or relationship to provide or receive troops between vassal and lord. In effect it was a system of tax farming by which the lord was appointed by the Sultan to collect the revenue of a set of land. The appointment was, in theory, non-hereditary and could be revoked by the Sultan. It could involve the actual management of the lands directly or simply a collection of the revenue by an absentee landlord. This supported an overall social structure which has been described as "agrarianate" which is to say that while the bulk of the economy was based on agriculture it was oriented towards and supported the development of towns and cities which were the focus of trade, politics, culture, education and so on.

Religiously...well, it's a bit all over the place. In the 10th century you had the Buyids who were actually ethnic Iranian Shia but who had a large contingent of Turkic horse troops dominant in the lands of central Persia. In the 11th century the Buyids are supplanted by the Sunni Seljuk Turks. This period, both in the political dominance of the Sunnis but also a number of religious and cultural innovations is sometimes called the "Sunni Revival" and, with the leadership of the Seljuks and particularly their ethnically Persian Vizier Nizam al-Mulk witnessed a number of institutional and religious developments that resulted in a Sunni Islam that looks a lot more like the orthodoxy we see today than what had existed previously, particularly in things like the relative entente between the four main schools of Islamic law, the scholarship of al-Ghazali, and the establishment of madrassas throughout Islamdom as major institutions of tertiary religious education.

Let me know if there are particular aspects of this that you'd like to know more about.

Source wise:

David Morgan's Medieval Persia and Marshall Hodgson's The Venture of Islam are both quite good on this.