To what was Edgar Allan Poe alluding by mentioning the superstition regarding black cats in his short story "The Black Cat"?
The line to which you refer is found in the fourth paragraph of Edgar Allan Poe's "The Black Cat." The narrator has explained his love of animals, and in this paragraph he describes his favorite pet, a black cat named Pluto. In part he says this:
In speaking of his intelligence, my wife, who at heart was not a little tinctured with superstition, made frequent allusion to the ancient popular notion, which regarded all black cats as witches in disguise.
The most common superstitious belief about black cats and witches is that these creatures are the "familiars" of the witches. A familiar can be any animal, though for witches the preferred animal is a black cat, and the familiar has an intimate understanding and knowledge of its specific witch. Some believe that witches cast spells through their familiars, and some believe the familiars are actually witches in disguise.
One modern example of familiars can be found in a popular book and movie series. The Harry Potter stories feature familiars; among others, Harry has Hedwig, an owl, and Ron has Scabbers, a rat. While they do not embody the characters themselves, as suggested by the witch superstitions, these familiars do seem to know their owners' minds and thoughts.
The narrator's allusion to witchcraft in his description of the black cat serves as a kind of foreshadowing for what Pluto does, and perhaps it is an early attempt to justify the narrator's later egregious behavior toward the cat.