The War of the Worlds is an amazing title if you want to sell your book – but kind of a bogus one. And The War of the Worlds did sell. It was more widely read than another book written in 1897 about the Earth and Mars. Around the time Wells was working on War of the Worlds, Kurd Lasswitz was working on Auf zwei Planeten, which literally translates to On Two Planets. Now, if you had a choice, would you rather read a book titled The War of the Worlds or one called On Two Planets? We'd rather read the one that mentions a war, so maybe the title did help the book sell.
Back to the content of the title, then. Let's start with the most obviously problematic part: "Worlds." Yes, there are two worlds involved here, but most of the action is really focused on a very small part of the earth: the southern part of England. In Wells' book, the rest of the world is basically unharmed, and they're only affected because they send aid to England. (Later writers imaginatively filled in this gap by talking about the invasion around the world, for instance, the aptly named War of the Worlds: Global Dispatches.) Hmm… why isn't this called "The War of Mars vs. Britain"?
"Worlds" in the title does make a bit of sense because the war does force everyone to re-consider the Earth's place in the universe. As the narrator points out, thanks to the war, people have a sense of the world as a single unit: the invasion "has done much to promote the conception of the commonweal of mankind" (2.10.8).
Now, "Worlds" might be the most obviously problematic part of the title, but we think there's something intentionally weird about the "The" in "The War." That might sound crazy, but seriously, what if that "The" were an "A"? "A War" implies that there's going to be other wars; by contrast "The War" says that there's only one war of the worlds and this is it (thank goodness). "The" sounds more definite and important.
But as the narrator notes at the end of the book, there might very well be more wars of the worlds. The Martians might've invaded Venus and maybe Earth will invade Venus too. Mars vs. Earth might actually be the First War of the Worlds, as this book almost promises there's going to be others. But that's an idea that comes at the end of the book. It's only when you come to the last few pages that you can see that the "The" in the title is potentially wrong. We've been reading the book as if it were about a singular event, but at the end we realize that this might just be the beginning. Tricked!