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.