Hawthorne is a very symbolic writer, and "Rappaccini's Daughter" is no exception. There's one overwhelming symbol in this short story, and it's carried throughout the work--the purple plant as sister to Beatrice.
The first time we see the purple plant is when Dr. Rappaccini is in the garden and draws near to the plant. When he does, he calls out for his daughter to come take care of it--despite the fact that he's wearing gloves and a mask for protection while she's wearing none. When we see her, Beatrice appears to be one of the flowers herself, both in skin tone and in dress. She is wearing a purple dress, much like the plant her father has called her to attend to.
Then, with all the tenderness in her manner that was so strikingly expressed in her words, she busied herself with such attentions as the plant seemed to require; and Giovanni, at his lofty window, rubbed his eyes, and almost doubted whether it were a girl tending her favorite flower, or one sister performing the duties of affection to another.
Beatrice approaches the plant with obvious joy, addressing it as her sister. She hugs it and tends to it as affectionately and kindly as if they were, indeed, sisters.
Over the course of the story, we learn that this is not so far from the truth. The purple-flowered plant was planted on the exact day Beatrice was born. It's constantly referred to as her sister, as well. The symbolism is too obvious to miss--they two of them are one, symbolically, and what happens to one will happen to the other.
Remember, Rappaccini could no longer touch the plant, for it had become too deadly for him. The same, of course, is true for Beatrice. Despite the fact that the evil doctor has "created" an Adam for his daughter Eve, she will not be able to go anywhere, do anything, or touch anyone outside the confines of this garden. What Rappaccini fails to understand is that he has created two monsters, and one of them will soon know it and hate him for it.