Labels are technically folders, if you have an email in your Inbox and you change the label to a folder, untick the Inbox label and the email will only appear in that "folder" from now on. If you leave both ticked then when you log into GMail on the folder the email will appear twice, once in the Inbox and once in the folder you selected.
I assume behind the scenes the emails are never actually "moved" just labelled to a folder name which is how it uses to display them.