Warning: Wikipedia contains spoilers.
The plot follows the adventures of the protagonists in the advanced experimental submarine The Nautilus built in secrecy and commanded by the mysterious Captain Nemo (the name means "no one" in Latin). Some observers thought the submarine to be a marine mammal, and three of the book's heroes were thrown overboard during the "hunt" for it. From there they were graciously rescued by Captain Nemo and travelled with him.
Their travels took them to numerous points in the worlds' oceans, some of them being known to Jules Verne from real travellers' descriptions and guesses, while others being totally fictional. Thus, the travellers witness both the real (and beautiful) corals of the Red Sea, the wrecks of the Battle of Vigo and the obviously fictional submerged Atlantis. Similarly, some of Verne's ideas about submarines which are laid out in this book turned out to be prophetic (such as the high speed and secret conduct of today's nuclear attack submarines), while others were less so (such as the need to re-surface every 48 hours to get fresh air).
(The word leagues in the English title is a literal translation of lieues, but purists prefer 20,000 Miles Under the Sea whereas twenty thousand leagues is sixty thousand miles (about 96,651 kilometres), and this distance is a measure of length, not depth.
Jules Verne wrote a sequel to this book: L'Île mystérieuse (Mysterious Island, 1874).