This unnamed song, known as The Haircut/Furcut song and I'm Going to Get my Hair Cut, is a song about Cookie Monster assuring Jeffy (a muppet boy) that haircuts don't hurt.
Jeffy: I'm going to get my hair cut.
I've never done that before.
I know I once cut my finger.
And I know I once cut my knee.
If cutting my hair's gonna hurt like that the barber's shop's no place for me,
But I gotta go get my hair cut.
Mom says I'm going to look so nice.
But when it's done, I'll look on the floor at the hair that was once on my head before.
It'll be all gone and I bet it'll never grow!
I'm getting my hair cut, but I don't wanna go!
(break while they talk)
Cookie Monster: Me going to get me fur cut.
Me gone plenty of times before.
It not like cutting me finger.
It not like cutting me knee.
'Cause cutting me fur doesn't hurt at all.
The barber's gentle as can be.
So me going to get me fur cut.
Me going to look so nice.
Me look in the mirror and me see a handsome monster. Oh, it me!
Me always get me fur cut when it grow.
Me getting me fur cut, and me so glad to go!
Both: We'll look in the mirror and we'll see a handsome monster. Oh, it's me!
It's fun to get your hair cut when it grows.
We're getting our hair cut and we're so glad to go.