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They're made from Melamine foam (and chemicals), which in itself is abrasive and wears away much like a pencil eraser. The warnings say do not use on highly glossy or satin finishes.
Just for grins, when I got a magic eraser a while ago I lubricated and brushed a small test section of paint. Looked OK until the sun hit it.
Fortunately, it was simple to fix with some rubbing compound.
Some people suggested it for leather too. Yeah, it gets it clean, but it wears right through the material and seriously reduces the life of your stuff.
I use mine for door sills as previously mentioned.
As mentioned above those magic erasers are a little abrasive and have some chemicals in them. Did you happen to take any pictures after the magic eraser?
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.