The coat of arms for the Montresor family shows an azure field with a human foot crushing a serpent that is biting it. This is particularly appropriate becuase it is Montresor who is attempting to exact revenge for the "thousand injuries" done to him by Fortunato. So while Montresor is represented in the coat of arms by the human foot, Fortunato becomes the serpent. Just as the foot crushes the serpent's head, Montresor will kill Fortunato. The motto is also appropriate because it reads "No one injures me with impugnity." Of course the motto can be applied here as well because there will be no impugnity for Fortunato; he will die in the caverns beneath the Palazzo of Montresor.
It is appropriate that Montresor describes his coat of arms and motto as he does, because it seems to reinforce the reader's conception of his great pride and vindictiveness. It seems possible, however, that his coat of arms and family motto are too appropriate, that he just invented them for his own amusement. He has been acting zany ever since he got Fortunato safetly underground. He claims to be a Mason and shows Fortunato the trowel with which he plans to immolate him. He may sense that Fortunato is subtly insulting him--which may be a habit with this man. Fortunato may be asking about Montresor's coat of arms in the hope of embarrassing him. Montresor may either not have a family coat of arms or else may have one that would indicate an inferior social status. Montresor is a French name. The family does not have roots in Italy that are comparable to those of Fortunato, who may consider Montresor a johnny-come-lately and may have let him know his contempt in various subtle ways in the past. His inquiring about Montresor's coat of arms may be Poe's way of showing an example of the "thousand injuries" so many readers have wondered about. Montresor wouldn't care about adding another lie to those he has already told this night. He lied about having the Amontillado, lied about being Fortunato's "good friend," lied about looking for Luchesi (since he wouldn't want to murder Luchesi), and lied about his concern for his "friend's" health. His entire description of his family coat of arms and the Latin motto meaning "No one injures me with impunity" may be a complete fabrication. After all, Fortunato will never check it out; he is doomed to be entombed and left to die that very night.