In Nathaniel Hawthorne's, The Scarlet Letter, the idea of living life openly is first seen in the way Hester wears her scarlet "A." She does not shy away from public, but lives a life trying her best to be Christ-like—as the society of Puritans expects—even though she is a "fallen woman."
The concept of the "burrs" is presented in Chapter 10.
...little Pearl paused to gather the prickly burrs from a tall burdock which grew beside the tomb. Taking a handful of these, she arranged them along the lines of the scarlet letter that decorated the maternal bosom, to which the burrs, as their nature was, tenaciously adhered. Hester did not pluck them off.
Burrs are rough to the touch, and here I would venture to assume that they reflect the harshness of Hester's existence as she wears the "A" upon her bodice without complaint or resistance. Neither does she brush off the painful "prickly balls" that Pearl uses to outline the shape of the scarlet letter. This reinforces Hester's acceptance of her life which centers around the pain of her humiliation, the knowledge of her sin, and her willingness to openly accept society's punishment.
I think the true nature of the burrs with regard to living openly reflects more directly upon Rev. Dimmesdale's inability to wear his "burrs" openly as Hester does. His sins (holding on like burrs) are hidden, and are all the more painful for it. As they talk about one's willingness to face the consequences of wrongdoing, Chillingworth asks about sinners:
"...why not reveal [their miserable secrets] here?"
"...they mostly do...And ever after such an outpouring, oh, what a relief have I witnessed in those sinful brethren!...How can it be otherwise? Why should a wretched man...prefer to keep the [sin] buried in his own heart, rather than fling it forth at one, and let the universe take care of it!"
"Yet some men bury their secrets thus," observed the calm physician.
Certainly Chillingworth is referring to Dimmesdale here. And though the preacher is not aware of Chillingworth's double entendre, his own sin haunts him. Dimmesdale suffers not only for his sin, but over his inability to face it publicly.
...it may be that they are kept silent by the very constitution of their nature. Or—can we not suppose it?—guilty as they may be, retaining, nevertheless, a zeal for God's glory and man's welfare, they shrink from displaying themselves black and filthy in the view of men.
Chillingworth—once more thinking of Dimmesdale—has little sympathy for the sinner, and expects them to expose their sin and "take up the shame that rightfully belongs to them."
The names burr and burdock, applied to the spiky little seed vessels of the hedgerow, were evidently bestowed with the poetic notion that the clinging burr was a miniature Sunball.
With this in mind, the burrs might also be seen as a source of "illumination," in this case, of Hester's sins.
Burrs, like sin, adhere to one and cause pain and grief. True bravery comes from wearing one's burrs outwardly—living an open life that shows one is willing to turn from sin—to then pursue justice, with all the world to see. Hester does this, while Dimmesdale cannot.