The Rani is a renegade Time Lady, a scientific genius whose villain status comes not from the usual varieties of lust for power and suchlike, but from a mindset that treats everything (including morality) as secondary to her research; she has been known to enslave entire planets in order to have a ready supply of experimental subjects and a place to carry out her experiments uninterrupted. Her major interest is in tinkering with other species' biochemistry - she was exiled from Gallifrey after some of her lab mice, as a result of an experiment, grew to enormous size and ate the President's pet cat.
The Rani was created in an attempt to give the Doctor another recurring foe like the Master, but in the event appeared in only two serials, The Mark of the Rani and Time and the Rani, before the series ended.
The Rani also appeared in Dimensions in Time, the Doctor Who episode created for Children in Need.