In 1988, he wrote a book called satanic verses in which one of the fictional character hallucinates the life of the Muslim Prophet Mohammed. In which, Mohammed initially chooses Hindu dieties instead of the Abrahamic religions (Moses/Jesus) as Islam's background before changing his mind and blaming the error on the devil.
The book is a FICTIONAL novel about two dudes who survive a plane crash and turn into angels and demons. And muslims heard about that one FICTIONAL passage about Mohammed and threw a fit. Thats it. Thats all there is to it. Absolutely insane that people cannot handle something so simple.
There's more to it than that.
Prostitute are given the names of the Prophet Muhammed's wives.
The Prophet Abraham who is highly revered in Islam, and is presented within an Islamic context in the book not a Judaic-Christian one, is directly insulted.
The angle Gabriel, again framed within the Islamic context and given his Islam name Gibreel, claims that God is "balding man wearing glasses that suffers from dandruff"
The supposed Prophet is Rushdie's book as he is dying he was a vision of a pagan Meccan deity, implying she is either real or that he believes her to be real.
A character named after the Prophet's wife, Aisha, claims she is receiving revelation from Gibreel (once more framed directly within the Islamic context) leads here people to drown in the seas based on this revelation.
There's some other stuff as well but I can't remember it all. Rushdie himself said he was aware prior to release that he'd cause a shitstorm with the book.