Skeuomorphs in UI design refer to interface elements that retain obsoleted visual or behavioral aspects of the physical objects they are based on. Take for instance the bumps in the F and J keys on the iPad virtual keyboard: they serve no particular purpose and are nothing more than artifacts of physical keyboards where similar indentations help provide sensory feedback to touch-typists.
Apple has been riding the skeuomorphism wave for more than a decade, alienating pundits and users alike in every episode, the most recent of which involves the redesigned iCal and Address Book in Lion, sporting a new skeuomorphic look heavily borrowed from their iPad sister apps, Calendar and Contacts.
The iOS-inspired interface came under harsh criticism, dismissed as an unnecessary gimmick and mocked for being hideous, even infantile. While the reaction seems quite disproportional to me, I admit that there are major arguments standing against skeuomorphism in UI design:
Potential false affordance; users may expect the skeuomorph to mimic the behavior of the original object in a particular situation. Failure to meet those expectations will result in frustration and discomfort. Try as you might, there is no way of browsing contacts by manually turning pages in the new Address Book, even though the interface strongly hints at this interaction. For more on affordance in general and false affordance in particular, check this out.
Visual noise that distracts users and negatively affect their productivity. Skeuomorphs are greedy for both screen real-estate and users' attention, obviously on the expense of efficiency and usability. The stitches in the iCal navigation bar illustrate this point like no other.
Functional limitations dictated by the original object may severely harm the user experience. The lack of a convenient three-pane view in the new Address Book is a perfect example.
Disorienting users as a result of using alien interactions that do not take advantage of the experience acquired through prior interactions with standard interfaces.
Alienating users with an excessive emphasis on aesthetics.
Out of all the factors above, the last one holds the lion share in this controversy; it's whether you love it or hate it. Obviously, when it comes down to pure aesthetics, subjectivity kicks in and renders the whole debate pointless.
When all is said and done, it is worth noting there is more to skeuomorphic interfaces than distraction and visual noise; they tend to have a powerful emotional impact on users, or more precisely consumers in the marketing speak. A contact management app that looks like an actual address book has more chances of establishing an emotional bond with its users and engaging them on the long run. Its distinctive personality might not always favor productivity, but that would be perfectly okay for an average user. In fact, the very tone of Apple's marketing is primarily emotional, and the skeuomorphic interfaces on both on iOS and on OSX perfectly serve Cupertino's agenda.
On my part, I can say that since Apple didn't tamper too much with standard controls, I can put up with, even slightly enjoy, using the new iCal and Address Book. In fact, the more I use them, the less I notice the interface, and that's quite a good sign if you ask me.