Yes, the film is quite closely based on the lives of a number of real life women in Ireland in the first half of the 20th century (though the effects continued well into the second half). The film is about just four women who are considered representative, but in fact a good many women (usually girls) were sent to the Magdalene Asylums or Magdalene Laundries, especially from the late 19th century onwards although the institutions go back to the 18th century. The usual reason for sending them was that they were 'sinners' (eg, unmarried mothers) or that their parents couldn't handle them. Some stayed there for the rest of their lives, having no idea of their rights and nowhere to go.
Several books have been written about this period, both historical works and accounts by survivors. Recently it turned out that the Irish government was formerly involved in this too; a public apology has now been offered to the remaining women.