A metaphor is a type of figurative language in which something is described as being something which it is not. It differs from a simile in that the device does not say that something is like something else, but rather that it actually is something else. However, as readers, we understand that a comparison is being made and that the description is figurative rather than literal.
In this story, the setting is arguably a metaphor in itself: the catacombs, covered with nitre, are like the web of a spider, and Montresor is drawing Fortunato deeper and deeper into that web. Montresor makes this explicit by pointing out the "white web-work," which he asks Fortunato to look at.
There are also some smaller metaphors in the language, such as where Fortunato's eyes are described as "two filmy orbs." Later, the narrator observes that "the wine sparkled in his eyes." This is not literally the case, but implies that Fortunato is looking increasingly drunk.
It could also be argued that the manner of Fortunato's dress is also a metaphor. He is in "motley," and his "bells" and jingling are remarked upon at several points throughout the story. The fact that Fortunato is dressed as a jester or a clown is metaphorical, indicating that he is in fact a fool, being unwittingly led into a trap without realizing that this is what is happening to him.
A metaphor is a literary device in which a thing is compared to another, usually dissimilar, object. For example, by calling a member of one's family a "black sheep," one is not claiming that relative is actually a sheep with black wool—it is meant to highlight how different they are from everyone else within the family.
The main metaphor in Poe's "The Cask of Amontillado" is the nitre along the catacomb walls. Nitre is a mineral form of potassium nitrate which grows in damp places like caves or cellars. The farther Montresor and Fortunato go into the catacombs, the more nitre there is growing along the walls. At one point during their journey, Montresor makes a metaphor by comparing the nitre to a spider's web:
"It is farther on," said I; "but observe the white web-work which gleams from these cavern walls."
This is rather cheeky and ironic on Montresor's part. The metaphor refers to how Montresor is entrapping Fortunato in his twisted revenge scheme. By pointing out the web-like patterns of the nitre, both Montresor and Poe are practically begging the audience to elaborate upon the web metaphor in their minds. Montresor is like a spider, the catacombs are his web, and Fortunato is the unfortunate fly about to be destroyed. The deeper the two men proceed into the catacombs, the closer Fortunato is to his doom.
Montresor warns Fortunato quite a few times about the niter that encrusts the walls of his family burial vaults (where the supposed pipe of Amontillado is being stored), knowing full well that Fortunato's pride and desire to rub Montresor's error in his face will compel his enemy onward. Montresor knows that Fortunato will believe he's made an expensive mistake in purchasing such a large quantity of a rare wine, and he also knows that Fortunato will not be able to resist gloating. When they first descend into the catacombs, Montresor tells Fortunato to "observe the white web-work which gleams from these cavern walls." In this metaphor, he compares the crusted niter to a spider web, adding to the ominous mood of the story. It is as though Montresor is the spider and Fortunato is the unwitting prey that becomes entangled in his figurative web. Montresor's metaphor seems quite menacing and horrifying when you think about its implications in this way.
There are a few examples of metaphorical language in "The Cask of Amontillado." For example, in describing the nitre (or "niter"), or a kind of chemical that is also called potassium nitrate or saltpeter, the narrator, Montresor, says, "It hangs like moss upon the vaults." This is a simile, a comparison that uses "like" or "as," a kind of metaphorical language. In this simile, the nitre, which forms in crystals that grow in encrustations, is compared to the growth of moss along the wall. Another metaphor occurs when the narrator says, "Here I knocked off the neck of a bottle which I drew from a long row of its fellows that lay upon the mould." In this metaphor, the bottle is compared to one of a series of friends sitting in a row.
Let us remember that a metaphor is a form of figurative language that compares one thing with something else, normally something that is very different from it. It is different from a simile because a metaphor asserts a direct comparison and does not use the words "like" or "as." If we examine this excellent story closely, we can therefore see that it contains a number of different examples of metaphors. The first one that I came across comes just as Montresor and Fortunato are entering the catacombs:
He turned towards me, and looked into my eyes with two filmy orbs that distilled the rheum of intoxication.
Notice the way that this metaphor compares the eyes of Fortunato to "two filmy orbs." Such a description, combined with the words that follow, serve to highlight the way that Fortunato is drunk and not in control of his actions--a fact that Montresor of course exploits to the full.