When to use it
You should unlink your device when you are no longer using ConquSync. If your account has been closed, deleted or expired and you don't unlink your device, your device will still try to sync. When it attempts to sync, you will receive an error. Since you are no longer using ConquSync, you should tell your device to not sync again by "unlinking" your account. This is not the same as temporarily setting the sync switch to off.
How to unlink
Go to Settings and tap/click on the Unlink button
What happens when I unlink?
Your device does no longer sync with ConquSync service. It also completely removes the ownership of your local tasks to the tasks on the cloud and those local tasks now belong to the "anonymous" user that is your device. This means that if you make any change to a task, that change will no longer be pushed to the cloud. If you later enter your login information again, it will start from "scratch" and send all tasks, projects, contexts, etc as if they were new.
Because of that, you should only unlink when you are no longer a ConquSync subscriber and not just to trigger the syncing process. The initial syncing is slow, as it needs to send all information, and by unlinking and linking back again, you are simply starting over every time.