Oh, my childhood, my innocent childhood! This is the nursery where I slept and I used to look out at the orchard from here! Look, Mother's walking in the orchard. In a white dress.
The speaker is Ranevsky, speaking in Act One. She has just returned to her estate after five years in self-imposed exile in France, and she and her family and friends are all congregated together in the "nursery," the room of her house where she and her brother Leonid grew up. She looks out the window at her beloved cherry orchard that is now in bloom, and momentarily thinks she sees her dead mother walking through it. Upon closer examination, she realizes that it is just a branch, whose white blooms looked like a woman's dress.
The passage shows two related things about Ranevsky, the protagonist of the story. First, the fact that she seems to undergo a hallucination shows her to be disconnected from reality. This is a defining character trait of Ranevsky, and much more than Lopakhin or Trofimov, it is her main antagonist in the story, the one thing barring her from achieving happiness. Furthermore, the content and location of the hallucination reveal the nature of Ranevsky's disconnect. She is seeking refuge in the past, her "innocent childhood." For her, the cherry orchard is a symbol of that past, the sight she would see through her bedroom window every morning, and the fact that she fantasizes seeing her dead mother walking through it merely confirms that impression.