If your Apple ID has been hacked, someone could use that to make purchases from the Mac App Store, the iOS App Store or the iTunes Store. Check your purchase history and credit card statements. Dispute any fraudulent charges with Apple... they should address the issue. If they don't, address it with your credit card company, but I don't think that will prove necessary.
Next, you need to ensure the security of your Apple ID. At a minimum, you need to change your security questions in addition to your password, and need to make sure the password is secure and that the security question answers are not guessable by someone who knows you slightly or who stalks you on social media. Preferably, replace those security questions entirely with two-factor authentication:
http://support.apple.com/kb/ht5570
It's possible the hacker got access through the e-mail address associated with your Apple ID, if that's a non-Apple address (ie, a separate account from the Apple ID account). You should change the password on that account as well.