If you were a kid growing up in America, you'd know instantly this was a reference to a 1936 Looney Tunes episode:

But that song was actually from a dude named Cab Calloway, which was featured in a 1936 movie called The Singing Kid (Calloway is the guy dancing on the ledge in front of the orchestra and comes in second):

Most of us can remember the first verse (the little owl sings it repeatedly before being cut off throughout the cartoon), but few can produce the full thing:

I love to sing-a
About the moon-a and the June-a and the spring-a,
I love to sing-a,
About a sky of blue-a, or a tea for two-a,
Anything-a with a swing-a to an "I love you-a,"
I love to, I love to sing!
Give me a song-a
About a son-a gun that went and done her wrong-a.
But keep it clean-a,
With a cottage small-a by a waterfall-a,
Any sob-a that will throb-a to a bluebird's call-a,
I love, I love to sing!
I was born a singin' fool-a,
Lah-de-dah!
Ol' Major Bowes is gonna spot me,
Got through Yale with boula-boula,
Lah-de-dah!
Old microphone's got me!
I love to sing-a,
I love to wake up with the south-a in my mouth-a,
And wave a flag-a,
With a cheer for Uncle Sammy and another for my mammy,
I love to sing!
The swingin'est,
Hot singin'est,
Bell-ringin'est,
Song singin'est
High tootin'est,
Sky tootin'est,
I love to sing!

Many of us would probably scratch our heads and couldn't make heads or tails of this, especially toward the middle. "Major Bowes" was the host of the Major Bowes Amateur Hour, a very popular radio show that lasted from 1934 to 1952, in which people would come on to display their talents, and often would be booted off with a bell. Similar to American Idol and is actually what the owl is doing in the Looney Tunes show. (Jack Bunny, who replaces Major Bowes in the cartoon, was a pun on Jack Benny, a well-known comedian at the time.) "Boula Boula" (misspelled here) was a fighting song at Yale. (The University of Oklahoma took their fighting song, "Boomer Sooner," from this.)

Oftentimes with history or literature is as a modern individual you only get the final South Park result. A person who's only seen that is so far removed from the original 1936 context that there's no way you'd understand it, and that moment just seems like a silly thing the creators made up. Half of the job for history or English professors is the attempt to dig through the words to find that original context, and sometimes it's impossible. There's no way you'd be able to go from South Park to Cab Calloway on your own. Or if you do, without outside resources you'd never figure out what Major Bowes or boula-boula are. Or if you're really ignorant, what swing, Yale, or Uncle Sammy are. Can you imagine trying to figure out the inside jokes from The Iliad and The Odyssey? Some people devote their entire professional careers to that, reading every snippet they can find and trying to connect the dots to create a larger picture. And unlike science, where eventually your experiment works, you know it'll never come to fruition without another discovery of more materials with new information, which almost never happens. But if you ever do line up all the dots, it's one of the greatest feelings in the world.