What is significant about the setting in Act I of Mrs. Warren's Profession?

The importance of placing the opening action of the play in a garden such as the one described in the text is its connection to the nature of English society.  One of  Shaw's main goals behind writing the play was to question or examine carefully the way that the British conceived of themselves versus what they were actually like in reality.

The cottage and the garden as described are the perfect picture of the image of genteel British society.  Carefully enclosed by a hedge to create a separation from the outside world and enclosing a world of propriety, a world where women are valued and clearly able to demonstrate their intelligence and value to the world.

Particularly when contrasted with the later setting in Vivie's office once the knowledge of her mother's profession has come to light and the nature of the way women are really treated in the "business world" has entered the play, the idyllic setting of the cottage seems naive and quaint and perhaps serves as a symbol of the way that British society wishes it was as opposed to how it really is.

Much of this information is explained in detail in Shaw's "Apology" that was written when the play was finally performed and in which he goes into great detail about his intentions.

What is the significance of "Mrs. Warren's Profession"?

Perhaps the single most important and significant feature of George Bernard Shaw's play, Mrs. Warren's Profession, is its frank and unsentimental treatment of the business of prostitution. 

In this play, Vivie is a typical "new woman," intelligent, well educated, and independent. As part of a new generation of women, and building upon a financial foundation that enabled her to attend university, Vivie is one of the first of a generation of British women to have the freedom to create careers for themselves in the male world of business. As various men propose to her, she begins to realize that marriage in her society is not greatly different from prostitution. 

Mrs. Warren represents an earlier generation and class. Brought up in poverty in a society in which one of the few professions open to women was prostitution, she has become the successful owner of a group of brothels. In a sense, both women represent the spirit of entrepreneurial drive, channeled into the paths available to their class and generations. 

The play addresses many of the double standards of British society of the period. The respectable rector, the Reverend Samuel Gardner, whose current wife refuses to even talk to Mrs. Warren, and was one of Mrs. Warren's former clients and the father of Vivie, is socially accepted, as is Crofts who is Mrs. Warren's business partner. 

Perhaps the most radical part of the play is the suggestion that work, whether in the form of Vivie's business or Mrs. Warren's brothels, is essential to women's character and happiness, and that the real problem with the double standard is the way it injures women's characters by trivializing them. Vivie states:

I know very well that fashionable morality is all a pretence, and that if I took your money and devoted the rest of my life to spending it fashionably, I might be as worthless and vicious as the silliest woman could possibly be without having a word said to me about it. But I don't want to be worthless. I shouldn't enjoy trotting about the park to advertize my dressmaker and carriage builder, or being bored at the opera to shew off a shopwindowful of diamonds.