What are the functions of possessive case?

The functions of possessive case nouns are:

To indicate ownership or possession.

the car of my mother = my mother's car

the teacher of our class = our class's teacher

the coats of the children = the children's coats

the covers of the books = the books' covers

To indicate origin or purpose.

children's shoes; not shoes belonging to children, shoes intended for children

ladies' room; the room isn't owned by a group of women, it's a room intended for their use

Shakespeare's plays are not possessed by Shakespeare, they're plays originated by Shakespeare.

yesterday's newspaper, a newspaper that originated yesterday