I always take it that "Part" usually means the order of a serialized story such that if you watch out of order, there are elements critical to the story that you did not yet learn, usually within the opening scenes of the story (think of a cliffhanger episode in a television show... while the second part usually opens up with a "Previously On" recap, that was for the sake of the fact that serial films and tv shows often had to deal with the fact that an audience may not be consistently able to watch the serial story).
In many classical literature, the story wasn't always told in a single bound copy. That was expensive. Many classic stories were actually first told in literary magazines one chapter at a time and then the story was bound into a single volume upon completion. Think like watching a season of a show at a rate of once a week only to go and buy the entire season on DVD or streaming and binging the whole thing. Many Charles Dickens stories were told in this fashion first. Robert Lewis Stevenson's "Treasure Island" was told in this fashion in a magazine for boys... which would explain the long part of the first chapter in which the narrator warns the reader that the story is not for the feint of heart... it was a disclaimer for the magazine warning the likely reader if they thought the story synopsis wasn't to their liking, they should not read it... because the original format had other stories they might like.
Generally here, the stories were told in chapters with each chapter ending on a cliffhanger which resolves in the next issue. Books that are published in a series might use "Part" to denote that the story is serialized over multiple books, when the typical series of books is episodic (In the 90s book Series, Animorphs, the books were largely episodic in the stories of the titular group. However, books 19, 20, and 21 were parts one, two, and three of a bigger story that was told in each book, and thus reading them out of order would mention plot details that were introduced in different books).
It could also be that the copy of your story binds two books that were originally intended to be separate books. In the comic book industry, comic books are typically sold individually but bound into trades (modern industry practices now tend to do this over a single storyline run) and denote this by showing the "Part" separation. This is often done after the book has aged a bit and likely reflects the idea that a store might have limited shelf space for a book series. If your book isn't the biggest seller, it might be best to settle for one book that has all three parts of the series bound in a single title rather than seperated and denote each book as a part. Other times, the book might actually be a collection of several books and use the internal note of "Book" to denote this. The Bible being the best example as the original texts featured in the Bible are not written together. Thus you have "The Book of Genesis" which is a distinct story (mostly of creation lore and early history with myth-like answers to the existence of things: How the earth was made, the fall of man, the first murder, the reason for languages) vs. Exodus (The Hebrew's flight from Egypt to the Holy Land).