So, uh, what's the deal with the 13-minute modern ballet sequence that has seemingly nothing to do with the rest of the movie?
The Real World: Hollywood
First of all, the "Broadway Melody Ballet" has everything to do with the movie. It's a dance representation of Don's story. Not that made-up mumbo-jumbo he rattles off to Dora Bailey at the beginning of the movie, but his real story—warts and all. That young hoofer in the yellow vest is a stand-in for Don.
Visually, the ballet sequence may be all bright and bold and Technicolored to the max, but, narratively, it's pretty dark. The hoofer comes up against menacing mobsters, gets his heart busted by a materialistic mystery woman, and has to wear a vest that makes him look like a banana. In other words, it includes all of the less-than-glamorous sorrows and struggles that Don encountered as he chased his dreams.
All of this symbolic honesty is significant. According to Cinema de Merde, the "Broadway Melody Ballet" is the emotional climax of the whole movie: "It represents the crucial turning point in Don Lockwood's ability to reveal his emotions and his internal crisis about his dramatic ability." Or, to nick a few words from MTV, it's when Don stops being polite and starts being real.
Dance it Out
Earlier in the film, Don tells Kathy that he's not good at expressing himself. "I'm trying to say something to you," he says, as they wander around the studio lot, flirting, "but I'm such a ham, I guess I'm not able to without the proper setting." Then he takes her on to an abandoned film set and tells her how much she means to him through song and dance in an improvised production number complete with fog and wind machines.
This earlier sequence suggests that the only way Don can express authentic emotion is through song and dance. So it makes sense that the "Broadway Melody Ballet" is how Don chooses to tell his true story; it's the biggest musical number in the whole movie. It's also no coincidence that the whole sequence looks like a stage production. Remember that Kathy kick-started Don's whole emotional evolution when she proclaimed the theater superior to movies.
In the end (and even if R.F. "can't quite visualize it"), Don's "Broadway Melody Ballet" pitch cements his emotional and professional growth. It also creates a tidy set of bookends for the narrative, if you ask us. The movie starts with Don telling an idealized version of his life story to Dora, and it ends with him relaying his authentic story through dance. Congratulations, Donny Boy; your evolution is complete.