How does the title of the play work as symbol and how does it reflect the role of women in society?

A doll is not a real person, it has no brain,living body,personality,identity or role other than a thing to be played with, to amuse, to entertain and discard when no longer interesting. In suggesting that Nora is in some kind of 'doll's house' Ibsen is also suggesting that she is an artificial creation with no autonomy and can only exist in an artifical world created specially for her. In some cases, in Ibsen's society and time (and our own at times) this was true. Women were idolized if they were from a wealthy family and pretty, for their beauty and charm, but given no means to further their own learning,training or independence in order to forge a career where they could stand on their own two feet. Under the guise of protecting women (who had been made deliberately dependent) society trapped them first by marriage and their role as 'wife' and then by child-bearing and their role as 'mother.' Many audiences just couldn't take Nora's walking out on this role. Some brave and ground-breaking women did break out to write novels or get involved in politics later on such as the Pankhursts but these were few and far between. The daily grind kept most women in the roles that had been created for them - in the doll's houses they lived in if they were lucky. If not they lived in 'doll's rooms' in poor areas of tenements but the role or lack of it was the same.Here is a history link to how some of these things began to change due to the bravery of some women breaking out of their 'doll house ' roles: