The Collaborative International Dictionary of English v.0.48:

Begum \Be"gum\, n. [Per., fr. Turk., perh. properly queen
   mother, fr. Turk. beg (see Beg, n.) + Ar. umm mother.]
   In the East Indies, a princess or lady of high rank.
   --Malcom.
   [1913 Webster]

WordNet (r) 3.0 (2006):

begum
    n 1: a Muslim woman of high rank in India or Pakistan