Technically, “skeuomorphic” design refers to software that mimics the elements in an older device that were functionally necessary for that device to work. In that way, the iPhone calculator’s three-dimensional buttons are an archetypal example of skeuomorphism. You needed three-dimensional buttons in physical calculators; on a flat screen, 3-D buttons aren’t necessary. (On the other hand, leather stitching in the Calendar app isn’t skeuomorphic, because the leather isn’t functional, just decorative.)
The iPhone calculator’s skeuomorphism doesn’t add any extra functionality to the app, nor does it convey any extra information about what the app does (as skeuomorphism does for Notes). Its only purpose, then, is emotional: The calculator’s three-dimensional buttons (which, it turns out, are a tribute to an iconic Braun pocket calculator) make the calculator feel approachable. This becomes obvious when you look at Windows’ calculator: Without the shadows on the buttons, it looks anodyne, lacking in personality. Now, I bet there are many readers who like that look, who feel that a calculator app should be anodyne. To me, though, that seems like an acquired taste, not a mainstream instinct.