The "I Want" song became a staple of Broadway productions in the 1930s and '40s: it's basically just the main character singing about his or her desires as a way of setting up the story. It's a slick way to get us into a character's mindset. It gets things moving, it tells us vital things we need to know about our hero or heroine, and it does so in a way that gets everyone tapping their toes.
The "I Want" song can be traced back to the mother of all Disney movies, Snow White and the Seven Dwarfs, with the famous "Someday My Prince Will Come" number about two-thirds of the way through. But most folks think it attained critical mass with The Wizard of Oz, a movie made to horn in on Snow White's action and which put its "I Want" song at the beginning of the story where it's really supposed to go.
We're betting you've heard it before.
Why are we bringing this up? Because Howard Ashman, who wrote the lyrics to all of the songs for Beauty and the Beast, was a big believer in the "I Want" song, and Judy Garland's version of it in particular. You can see examples of it in his earlier works: Little Shop of Horrors (which actively evokes Miss Judy with its "the rainbow's just a no-show" line) and The Little Mermaid, who just wants to be part of your world.
For Beauty and the Beast, the "I Want" song (called "Little Town") fills us in on two of the three main characters: Belle, the oddball outsider in her little town, and Gaston, the inexplicably beloved town bully who makes his intentions for Belle crystal clear. (If this guy lived in modern times, we're guessing he'd end up on the wrong end of a can of mace after trying to grope the homecoming queen in the back of his dad's '73 T-Bird.) It's a five-minute song; by the time it's done, we know everything we need to about who these people are and how they fit into this world.
It's not shy about its The Wizard of Oz influences, either. Notice Belle's blue and white dress, eerily similar to that of Dorothy Gale. And, in case we missed the reference, they give us a reprise actually set in a barnyard. Beauty and the Beast definitely does its own thing with the idea, and it's not afraid to wear its influences on its sleeve.
It pays to know where the song came from and how earlier movies helped inspire this one.
Howard would want it that way.