At the end of chapter one, the narrator points to the rosebush that grows beside the prison door. He speculates that the rosebush might have sprung up from the footsteps of Ann Hutchinson - a woman persecuted, like Hester will be. He does directly tell us, however, in the final line of the chapter that the rose symbolizes a "sweet moral blossom" to "relieve the darkening close of a tale of human frailty and sorrow." In other words, the narrator tells us that the rose will symbolize a lesson to be learned in the midst of this tragic tale. The narrator confirms this idea of a moral coming from the story in the final chapter. He says one of the morals that can be learned from the story is "Be true! Be true! Be true! Show freely to the world, if not your worst, yet some trait whereby the worst may be inferred!"
The Rosebush is definitely worth a closer look. Note also where it grows: next to the prison. It symbolizes nature's endurance and impartiality in contrast to human affairs. In a narrative that has such dark undertones of sin (Hester and Dimmesdale) and evil ( Chillingsworth) and their respective impact on the human condition, the rose is indeed a "blossom" that has enduring neutrality while the whole Puritan community is judgemental.
The roses represent freedom outside of the jail. They also represent Hester's growth because they start off as buds and then blossom. They also bring color to a black and white society. The roses also bring happiness to Pearl. The roses negatively represent mocking and shame because Pearl throws them at Hester and laughs mockingly. They also represent darkness because the graves have roses and they always seem to be in dark settings.
I see the rose representing first and foremost Hester, the mother figure. Pearl says she was plucked from a rose bush (which breaks off into many other directions as well). Also, in the garden at one point, Pearl reaches for a rose and cries when Hester tells her no. She wants to feel secure in motherly arms.
Another symbolization would be that the garden aforementioned represents the Garden of Eden, and the rose bush is the Tree of Knowledge. Pearl, aka Eve, wants to get the "apple" on the tree, which is a sin.
In this Garden, Hester tells Pearl, Eve, not to take the rose, apple, and is therefore in the shoes of God. This is also shown on the scaffold, where Hawthorne describes Hester as having a halo.
However, we have already established that the rose represents Hester, and the rose represents the apple, which is sin/temptation/evil.
Therefore, Hester is the epitome of sin/temptation/evil. This puts Hester in the role of Satan. So Hester is now both God and Satan.
This leads to the theme that in everything good, there is something evil.
But that's just my thoughts :)
The Rose also Symbolizes the Defiant attitude of Pearl..