The de-authorize button in the Manage Devices section of the web interface cuts off access to the SpiderOak servers from a device. Once you de-authorize a device, the SpiderOak application on that device will report that it is disconnected. A de-authorized device will not be able to connect, upload, download, sync, share, or delete anything. The web interface gives no feedback and might leave you with the impression that it didn't work (that's something on our list of things to improve) but it does indeed de-authorize it.
If you lose a device or it is stolen, you should immediately de-authorize it so that no one can use it to access your account.
If you later recover your device, or accidentally de-authorize a device, you can reauthorize it by deleting your application data folder on the de-authorized device, then running SpiderOak again. SpiderOak will prompt you for the email address associated with your account and your password when it restarts, and you can choose that you are reinstalling the de-authorized device. After syndication completes, SpiderOak will reopen and you will be able to continue using this device normally.
For instructions on how to delete your application data folder, see How do I manually uninstall SpiderOak?