Way back when, movies and teevee shows and books and whatnot used to be pretty much self-contained items. But nowadays, in a lot of cases, as specific movies and teevee shows and books and comics branch out into multiple sequels and spinoff series and all of their sequels, what becomes important isn't so much the original story. Instead, the entire setting of the story takes primacy. Thus, a Universe is born.
At what point does a fictional setting become a universe? Star Wars takes place a long time ago 'in a galaxy far, far away', but at what point did it become possible to talk about the Star Wars Universe? My guess is that it was when other stories started to be told there, other than the original three movies. The emergence of the Star Wars universe seems to me to have arisen in the mid-1990s, when, on the heels of Timothy Zahn's Thrawn Trilogy, a whole bunch of new books started coming out...and then comics...and then games...and all this before the Prequels started even shooting. Star Wars had become a Universe.
The same thing happened to Star Trek, when it went from being the adventures of a specific crew of a specific ship to also including the adventures of another crew, 80 years later, and then the adventures of the crew of a space station, and then the adventures of...you get the point.
And then there are the big comics publishers, Marvel and DC, both of whom have their own universes. All their respective superhero books take place in the same world, so that there can be crossover appearances that take characters from one book into another. It's not enough to have Spiderman having his own adventures; no, every so often he has to have a run-in with, say, Daredevil or the Hulk or whomever. Most times this is just fun name-dropping, but it's also a subtle way for the comics companies to cross-market their other books, the ones you might not be reading.
Famously, the DC Universe became extremely cluttered and complicated over the decades, until the point where the Powers-That-Were decided to do a big storyline in which the entire universe would basically be re-booted. Apparently this didn't take, as there have been several reboots since the original Crisis on Infinite Earths. Meanwhile, Marvel's Universe, while not so complex, was still plenty crowded -- which allowed Marvel to make money a few times by putting out a Complete Guide to the Marvel Universe, or something like that, which was basically an encyclopedia of just about everybody. And Marvel, too, had its Giant Enormous Crossovers, which they called Secret Wars.
In Firefly, the characters actually refer to their Universe, by calling it "the 'Verse". Oddly, nearing ten years after the show's brief run, the Firefly universe is among the most beloved and yet least explored; all we have are fourteen teevee episodes, a movie, and three graphic novels. That's it.
So, what's the difference between a Universe and a 'World'? For instance, nobody talks about the Lord of the Rings Universe. They refer to its world, or even to the world by its name, Middle-Earth. A Universe seems to me a primarily science-fictional concept, and needs more than one planet to be properly a Universe. But why a Universe, and not a Galaxy? Well...who knows? I personally like the word "Galaxy" better, but what if you start mucking around with black holes and stuff in other Galaxies? What if you start to dink around with multiverses? Aieee! It makes the head explode!