I've only come across this in sentences like "She could sing the phone book and I'd pay to listen" (or any of numerous similar variants). The idea is that the phone book (a list of people's names and numbers) would be an extremely dull thing to sing, so anyone who could make it worth listening to must have a fantastic voice and generally be a great performer. Of course, it's not meant literally.
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The first time I heard this was on "American Idol"--judge Randy Jackson would use this phrase a lot to critique performers he thought were especially amazing. The contestants later poked fun at him for this by actually singing entries from the phone book.
This is a quote by Richard Carpenter about the singing ability of his sister Karen Carpenter.
i.e.: she could make anything sound good
I totally agree. Karen Carpenter voice is such a joy to hear for her femininity just shines.