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Every computer that's currently connected to your Dropbox account and syncing changes is listed on the administrative screen.
You can add a computer here (although it's generally easier to do so from the client side). You can also change the name of a computer to make it more descriptive.
That Unlink option ends the synchronization relationship between the client software on that computer and the Dropbox web folder. It doesn't delete the files from that computer, only prevents further updates from being made.