Axel, begins by explaining that Otto Lidenbrock has discovered a manuscript written by a 16th century Icelandic man. The manuscript claims to describe a path to the center of Earth. Axel and Otto then travel to Iceland in order to begin their journey to the center of Earth. They arrive in Reykjavik, Iceland and then travel to Mount Snaeffels in order to begin their descent. From this point forward, the novel's setting locations are fictional places within Earth's interior. Then the explorers finally make their exit through Stromboli's vent in Italy.

I'd like to point out that the previous post states that the explorers exited through Etna on the island of Stromboli.   That is incorrect. Etna and Stromboli are two different volcanoes located in Italy. Stromboli is a small island located north of southern Italy's mainland. That's where Etna is located. If a reader checks the text, Axel and Otto are told by a local shepherd boy that they are on the island of Stromboli. The men then look south and see Etna in the distance.

And those rounded blue hills to the east were the mountains of Calabria! And that volcano on the southern horizon was Etna, terrible Etna itself!

"Stromboli, Stromboli!" I repeated.

As for the year that the book takes place, readers are told that Otto discovers the manuscript in the spring of 1863. The journey begins from that point.

The novel takes in various settings around and under Europe. It begins in Hamburg, Germany, where Axel lives with his uncle. From here the two set out to Sneffels, an extinct volcano in Iceland, and venture down its crater to begin their subterranean journey. Along with their guide Hans, they travel many miles underground, under Europe, encountering various wondrous places along the way such as a subterranean ocean and primeval forests. Finally, they emerge through an active volcano, Mount Etna, on the island of Stromboli, Italy.

It is only when they arrive back on the surface of the earth that Axel suddenly realises what an amazing journey they have been through.

Oh, what a journey! What a wonderful journey! We had gone in by one volcano and come out by another, and this other was more than three thousand miles from Sneffels, from the barren country of Iceland at the far limits of the inhabited world! The chances of our expedition had carried us into the heart of the most beautiful part of the world! (chapter 42)

The journey, then, has been an extremely varied one, encompassing vastly different regions on the surface as well as below ground. 

Large portions of the setting for this story are fictional. At the time that Verne wrote this book, geologists were not sure what the interior of Earth was like. In typical Verne fashion, the text weaves known science with fiction. After descending through a volcano into the Earth's interior, the setting is fictional locations inside Earth. Regarding actual locations, the story begins in Hamburg, Germany in the spring of 1863. The story begins with Axel explaining to readers that Otto Lidenbrock had discovered a manuscript written by a 16th century Icelandic man. The manuscript supposedly narrates a path to the center of Earth, and the path begins at Mount Snaeffels in Iceland. The men then travel to Reykjavik, Iceland in order to gain access to the starting location. The story ends with the men being ejected from Stromboli's vent in Italy.

The setting is important mainly because it gives readers a believable exploration story. Readers know that hollow spaces exist in Earth. Big caves and caverns have been known about for centuries. Additionally, it makes a certain amount of sense that the throat of a volcano could give a person access to Earth's interior. Unfortunately, Earth's interior is not nearly as full of big, hollow, and open spaces as Verne's story would lead us to believe, but it still makes a great story.