That, my dear anon, is one of the great unsolved mysteries of ALW Phantom.
I mean, assuming that you’re asking why there’s a monkey music box *at all*.
If you’re just wondering why it’s in the Prologue, it’s because it belonged to the Phantom and was found in his lair by the mob, to eventually end up in the auction of old stuff from the Opera’s storage rooms. And then old!Raoul bought it because he remembered Christine talking about it in one of her stories of the Phantom.
But, as for the actual *presence in the Phantom’s lair* of a music box in the shape of a barrel organ with an attached figure of a monkey playing the cymbals–your guess is pretty much as good as mine.
If we’re talking about the 2004 movie, it’s really straightforward: in the movie, the Phantom had a stuffed toy of a monkey with cymbals while he was imprisoned/exhibited as a child (probably an item that he got by chance after it was discarded by someone else), and seems to have upgraded to a more deluxe model after moving into the Opera house. But this applies only to the movie, as there is no mention of the Phantom in the stage musical having had any such toy, and he was imprisoned *as an adult*.
Some people think that the music box is meant to symbolize the character of the Persian Daroga, who was extremely important in the original book but deleted from the musical/combined with Madame Giry. This is mainly due to the description of the monkey as wearing ‘Persian robes’, and the fact that it’s apparently a ‘friend’ to the Phantom. I’m not a fan of this theory because it seems like an extremely arbitrary way to reference a character that ALW doesn’t seem to have given a second thought for.
I have a ~kind of/sort of~ theory of my own, the basis of it being that perhaps ‘Masquerade’ could be a bit more diegetic than we tend to think of it as. In this scenario, then, the Phantom has heard and is familiar with this song about masks and hiding ones face, and has latched onto it in an ironic sort of way (like how Leroux!Erik internalizes the whole ‘living corpse’ thing, to the point that he sleeps in a coffin). So then he finds this music box that plays his ‘favourite’ song (and happens to have a monkey on it–cymbal-playing monkeys being a cliche sort of automaton), and takes it home to his lair so he can listen to it whenever he wants to. (Yeah, there’s still holes in this theory, but it makes as much sense as anything else I’ve been able to come up with about the music box.)
I would really like to know what ALW/Hal Prince/Maria Bjornson/whoever’s idea it was actually *intended* with the music box/monkey, but as far as I know no one has ever said anything about it?
There’s also the mystery of why it starts playing by itself at opportune moments, apparently of its own volition (unless the Phantom *wanted* Christine to wake up and unmask him while he was busy composing). I wonder how many times that thing went off by itself and almost gave old!Raoul a heart attack. Maybe the REAL Opera Ghost is *inside* the music box: perhaps it’s possessed by the disgruntled spirit of the Daroga, angrily clinking his tiny cymbals and demanding that people stop cutting his role from the story. The world may never know.