iTunes Store: Associating a device or computer to your Apple ID - http://support.apple.com/kb/HT4627 - In connection with, "When you turn on iTunes Match or Automatic Downloads, or when you download past purchases on an iOS device or computer, that device or computer becomes associated with your Apple ID." "Your Apple ID can have up to 10 devices and computers (combined) associated with it. Each computer must also be authorized using the same Apple ID. Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days." - Additionally instructions for "Removing an associated device or computer from an Apple ID"
It's done that way because the media owners who can tell Apple what to do don't want people going around to their friends' houses and downloading all their iTunes music on the friends' computers too. If you're going to share a computer make sure you avoid doing the things listed above that will cause this message to appear. Keep a backup of your purchases on an external drive.