Common shorthand for both the University of North Carolina (UNC, at http://www.unc.edu, in Chapel Hill) and the University of South Carolina (USC -- wait, not SoCal -- at http://www.sc.edu, in Columbia). There is a minor rivalry between the two universities, complete with lame cheers a la "When you say 'Carolina' say 'North Carolina'; when you say 'Carolina' say 'Heels!'"
It is likely rather infuriating to the South Carolina folks that when sportscasters talk about "Carolina," particularly in the basketball context, everyone knows to whom they're referring -- and it's not them.