The significance of the transition from street to catacombs in "The Cask of Amontillado" is to heighten the suspense and create a atmosphere of uncertainty and fear. Poe is a master at finding a way to frighten us when we least expect it. He draws us into a story only to transition us into horror. I don't care for straight horror. I like the creative, unexpected horror that you find in Poe and in Sci-Fi like Twilight Zone.
The ordinary, in "The Cask of Amontillado" suddenly becomes horrific, when we realize that Fortunato is to be murdered, much more frightening than a simple slasher type murder.
When Montressor brings Fortunato down into the Catacombs under the pretense of tasting a fine wine, this is ordinary. What really awaits this hapless victim, is his merciless death. What could be more horrific or frightening, certainly more so that a direct assault on the senses.
The sneaky, deceitful murder is much scarier than the one that is clearly identified as a threat. This is what Poe does for us in his work, he is subtle, lulling the reader into the story, then wham, he brings out the macabre and the reader is caught unexpectedly terrified.
"My heart grew sick - on account of the dampness of the catacombs. I hastened to make an end of my labor. I forced the last stone into its position ; I plastered it up."
The street symbolizes the everyday world in which the characters live. As the men descend into the catacombs, it is like delving more and more into the mind of Montressor. It is in this place that he intends to carry out his revenge for some insult put upon him by Fortunato. The deeper they go, the more intense Montressor's mood seems to become. He talks of his family motto ("No one who insults me with impunity") and his family crest, which depicts a golden foot stepping on a snake which is biting the heel of the foot. These symbolize the action that Montressor intends to carry out: revenge. The world above ground would not have been an appropriate place for the story as it represents the everyday world to which many people have access. He would have been found out. By moving to the catacombs (and the inner recesses of Montressor's mind), the murderer is more likely to get away with his scheme.
Also, the two worlds are linked through Fortunato's costume. There is a masquerade taking place in the streets, and Fortunato is costumed as a fool. This is ironic because he is about to be fooled into following a man into the catacombs and be murdered.