The Haji Ali Dargah was constructed in 1431 in memory of a wealthy Muslim merchant, Sayyed Pir Haji Ali Shah Bukhari, who gave up all his worldly possessions before making a pilgrimage to Mecca. Hailing from Bukhara, in present-day Uzbekistan, Bukhari travelled around the world in the early to mid 15th century. He travelled to India with his brother and finally reached Mumbai – near Worli. He then decided to reside there permanently for the spread of Islam.
Until his death he kept spreading knowledge about Islam and his devotees would regularly visit him. Before his death he advised his followers that they should not bury him in a graveyard but should drop his shroud ('kafan') in the ocean and should be buried by the people where it is found.
His wish was obeyed by his followers. That is why the Dargah Sharief is built at the very site where his shroud came to rest in the middle of the sea where it perched on a small mound of rocks rising above the sea.
There is another mausoleum built across the bay. It is believed to be the tomb of Ma Hajiani, the sister of Haji Ali. This mausoleum was built in 1908 in honour of Ma Hajiani, a saint believed to be the sister of Saint Pir Haji Ali Shah Bukhari.
According to legend, they died at sea and their bodies were washed ashore, a few metres from each other. They were then buried at the respective spots they were found. Subsequently, two tombs were built — Haji Ali for the brother and Ma Hajiani for the sister. At the Ma Hajiani Dargah, women frequent in large numbers, making offerings of red or green glass bangles, red indicating one’s wish for marriage, and green for offspring.
Above info sourced from Wikipedia and an article in The Hindu.