Let's begin with a definition of an "allusion." An allusion is a a reference in a literary work that references something else without saying so directly. Often (but not always), allusions are cultural or political references. (It can sometimes be difficult to "get" these types of allusions when they are no longer culturally relevant.)
However, allusions in Western literature will often be to mythology, the Bible, and other well-known works of literature. This is the case in Poe's classic poem "The Raven."
The first allusion in the poem is a nod to mythology. In line 41, the speaker notices the raven, "Perched upon a bust of Pallas." "Pallas" is "Pallas Athena," the Greek goddess of wisdom. The fact that the raven chooses to sit there, upon her head, rather than anywhere else in the room, might be interpreted in a couple of ways. First, it might be taken ironically. The bird only seems to know one word. The speaker may be attributing, in his idolatry of Lenore, more wisdom to her than she deserves. Or it might be positive, in that both Lenore and Pallas are wise. Both are certainly worshiped.
Another mythological allusion occurs in line 47, in which the speaker demands of the raven to "Tell me what thy lordly name is on the Night's Plutonian shore!" Pluto is the Greek god the Underworld. The underworld, (also known as Hades or Hell) is perpetually dark. The darkness here works as a metaphor for the speaker's state of mind which is filled with thoughts of death.
The word "shore" may also be an allusion to the River Styx, which existed between the Earth and the Underworld. The river was piloted by Charon, the ferryman who carried recently-deceased souls from the earthly shore to that of the Underworld. This too makes sense, given the speaker's internal torment.
Line 80 contains a biblical illusion. The air in the speaker's bedroom becomes oppressive and he senses that it was emanating from a "perfumed from an unseen censer / Swung by Seraphim whose foot-falls tinkled on the tufted floor." In the Hebrew Bible, these creatures are six-footed and winged. They continuously fly around God's throne, saying only one word in repetition: "Holy, holy, holy!" In this way, they have something in common with the winged raven, whose single word is "nevermore." Like Pallas Athena, however, the allusion might be negative and not positive. Although the seraphim are holy and perfumed, the sense is that they are oppressive, not comforting.
Another biblical illusion is found in line 89. The speaker cries out, saying, "is there no balm in Gilead?" This is from Jeremiah 8:22: "Is there no balm in Gilead; is there no physician there?" The "balm of Gilead" is a real thing. Mentioned several times in the Bible, it is made from the gum of a bush that grows plentifully in Gilead (an area East of the Jordan River.) It is rather an all-purpose healing compound, used to treat a variety of ailments, from cuts, to bruises, to burns. In addition to its medicinal uses, the "balm" is also meant to be understood spiritually, something to soothe one's emotional wounds. Clearly, the speaker here is seeking the spiritual comfort such a balm would bring.