I haven't read it yet, but I have done a lot of planned research before I start to read it in the near future.
But as far as I know--
Filled with Anglo-Indian references, it starts off with two men transforming into angels, Gibreel (Gabriel) and Saladin (the Devil) as they fall from the sky, after militant Arabic terrorists hijack and blow up an airline plane flying over London.
Then it goes into dream sequences and back and forth history switching.
Ultimately, it's a satire on Islam. When Mahound (Mohammed) first preached Islam, it was not widely accepted or tolerated in the ancient Middle East filled with pagan idol worshipping. In order to gain tolerance, Rushdie suggests that he compromised his stance on monotheism, by deifying three street prostitutes as Islamic goddesses. Only to realize that he might have taken the advice to do so from the Devil (disguised as Gibreel).
What makes this novel controversial is that no one has ever satirized the Islam religion. It has been done so with Christianity for ages, with the Medieval Passion plays, Jonathan Swift, Shakespeare, John Dryden.
But Muslim took everything sacred and seriously. Thus, they were personally insulted by a book that mocked everything they believed.