What is Begum?

Legal Definition
Begum, begam, baigum or beygum (Turkish: begüm, Persian: بیگم‎‎, Urdu: بیگم‎, Bengali: বেগম) is a female royal and aristocratic title from Central and South Asia. It is the feminine equivalent of the title baig or bey, which in Turkic languages means "higher official". It usually refers to the wife or daughter of a beg. The related form begzadi (daughter of a beg) also occurs.

In South Asia, particularly in Punjab, Sindh, Hyderabad, Delhi, Khyber Pakhtunkhwa and Sylhet, begum has been adapted for use as an honorific for Muslim women of high social status or as a surname.
-- Wikipedia
Legal Definition
In Indla. A lady, princess, woman of high rank.
-- Black's Law Dictionary