The first two things any community makes, according to the narrator of The Scarlet Letter by Nathaniel Hawthorne, are a cemetery and a prison. This is an indication, of course, of two things that never change in human nature. First is man's tendency to sin and society's need to punish; second is the inevitability of death for all men. It is the prison door which captures our attention for this question and, until the end, this novel.
Right next to the prison door, on one side and almost flush against the threshold of the prison, is a wild rose bush. Every prisoner who goes in or out of the building must see it. To the criminal (sinner) who enters the prison, it is a "fragran[t] and fragile" reminder that beauty still exists; for the "condemned criminal as he [comes] forth to his doom," the sight of the delicate petals is a reminder of Nature's pity (sympathy) for him.
The narrator tells us this rose bush "has been kept alive in history," though he cannot attest to the source of its being there and will not presume to guess. He does say, in the last words of chapter one:
Finding it so directly on the threshold of our narrative, which is now about to issue from that inauspicious portal, we could hardly do otherwise than pluck one of its flowers and present it to the reader. It may serve, let us hope, to symbolize some sweet moral blossom, that may be found along the track, or relieve the darkening close of a tale of human frailty and sorrow.
In the narrator's words, then, the rose symbolizes a luminescent (bright) touch of morality in this story, or perhaps it will serve as a pure and colorful spot of relief in this woeful tail of "frailty and sorrow." Another way to look at the rose is as a symbol of hope to all who leave or enter the prison, a place which represents sin, condemnation, and punishment. It is as if Nature wants to offer at least a glimmer, a fragile petal of hope to all who feel hopeless and condemned.
As the story progresses, the rose serves as a kind of relief from the weight of darkness and sin.