A sultanate is a state, territory, or office ruled by a sultan, a title used by Muslim sovereigns. The Arabic word sultan originally meant moral or spiritual authority and later came to mean political power. From the 11th century it became a royal title: Mahmud of Ghazna (reigned 998 to 1030) was the first Muslim ruler his contemporaries called sultan, and the Seljuqs made it a regular title that spread across the Islamic world.
Well-known historical examples include the Delhi Sultanate and the Ottoman Empire, whose rulers were sultans. Sultanates still exist today: Brunei and Oman are sovereign sultanates, and several Malaysian states are ruled by hereditary sultans.
Source: Encyclopaedia Britannica: Sultan
Image: Omar Ali Saifuddien Mosque, Brunei, by Mx. Granger, CC0, via Wikimedia Commons.