A fold-song is any song sung while folding something, usually clothes. What else can you fold? Well, I sometimes like to sing when I'm folding my hands and occasionally when I'm folding thoughts in my head although that's a more abstract type of folding.
Here's another type of folding. I work in an office and when I'm doing filing or making labels for folders I like to think of this work as "folding" - of course, I usually sing to my self while doing this.