Edgar Allan Poe's poem "The Raven" is written in the first person and narrated by a young man mourning the death of his "lost Lenore." He appears melancholic by temperament as well as greatly saddened by the loss of his beloved. In the lines cited, he is asking the raven whether there is some cure for the sorrow he is feeling or whether he is condemned to mourn for the rest of his life.
The specific excerpt "Is there—is there balm in Gilead?—tell me—tell me, I implore!” is a reference to this passage from the Old Testament:
Is there no balm in Gilead; is there no physician there? why then is not the health of the daughter of my people recovered (Jeremiah 8:22)?
A balm in this context means a curative medicine. The town of Gilead was famous in the period of Jeremiah for offering such medicines. Thus, the significance of the reference is that the student is desperately seeking some form of cure for his sorrow and asking, in an allusive manner, whether there is any medicine or cure that might help him.
"Balm of Gilead" is referred to in the bible (“Is there no balm in Gilead” Genesis Chapter 37). Literally it refers to a specific healing substance produced by a plant that grows in Gilead, which was carried by merchants to the men who sold Joseph. In Poe’s poem it refers to a substance that can heal a broken heart. “Balm of Gilead” is a frequent allusion in literature, referring to a mythical healing substance that can never be found; it bespeaks a loss in values or goodness.
Because the balm is typically viewed as a remedy for those with broken hearts, it would make sense that the narrator in The Raven would want such a remedy as he is lamenting Lenore.
The balm of Gilead was also viewed as something of great value and not necessarily easy to obtain. Poe includes this reference to indicate the narrator's desire for hope. Authors often include allusions to the balm of Gildead for this same reason. Think of it like this--if there can be a possibility of mending something you have badly broken (a heart in this case), wouldn't that give you some hope? Some desire to keep on living? That is what the narrator is looking for in this passage, as unlikely as it is.
In this excerpt from Edgar Allan Poe's "The Raven," what does the biblical reference to the healing “balm in Gilead” signify?