Henrik Ibsen's choice of the title A Doll's House, rather than "The Doll's House," signifies a quantitative reference. In other words, Ibsen's choice refers to quantity. The word "the" is referred to as "the definite article" because it is the only English language article that is used to point to a very specific noun (Parts Of Speech, ESL Resource Center). For instance, if we say "the cat is sitting on the mat" we are verbally pointing to a very specific cat on a very specific mat. Furthermore, if we were to combine the definite article "the" with a singular noun, such as doll's house, we are also referring to one, and only one noun, or doll's house. Thus, if Ibsen had chosen the title "The Doll's House" he would be pointing to one very particular "doll's house" and only one particular "doll's house."
But that was not Ibsen's intention. Ibsen wrote the play A Doll's House to protest the treatment of women in his society. Ibsen saw all women, especially middle class women like Nora, as being treated like "dolls." Ibsen saw that society was denying women the basic human rights of education, financial freedom, and even basic respect. Thus, Ibsen wanted to incorporate all women and all "doll's houses" into his play and into his title.
Let us now look at the English language article that Ibsen did choose for his title, the article "a." While the definite article "the" refers to only specific things, the article "a" refers to general things. For instance, in the famous phrase "My Kingdom for a horse!" the article "a" tells the reader/listener that any old horse will do. The writer/speaker is not referring to any single horse, but any horse at all (Articles, Determiners, And Quantifiers, Guide to Grammar and Writing). The same idea applies to Ibsen's title A Doll's House. His title refers to any woman's home, or "doll's house," and it can even be applied to all women's homes or "doll houses."