Young boy is dying.
Barbara spurns him, then dies too.
He's the rose, she, thorn.
The Wikipedia entry for this old song contains a priceless reference to the 1690 broadside edition, which titles the song as "Barbara Allen's cruelty: or, the young-man's tragedy. With Barbara Allen's lamentation for her unkindness to her lover, and her self". And that's the essence right there: Barbara Allen spurns the love of a man, or a boy, as there are many versions of the song out there since its first known reference by Samuel Pepys (again, according to Wikipedia) in 1666. The guy dies of heartbreak, whereupon Barbara regrets her decision to deny a man life through her lack of love. At this late juncture, she falls in love with him, and of course, she dies too. From his grave comes a rose, her's the briar, and through their intertwining they at last discover fidelity and love. Too late, if you ask me.
Here's a Dylan performance from some time between 1988 and 1991.
And here's the version that Dylan recorded in 1962 at the Gaslight Cafe in 1962, which was where this song was commercially released a few years ago.