The contact has now been unsubscribed and you are protected from accidentally emailing them. The contact will still show in your account, so you don't lose any valuable information, however it will not count towards your billing. You will not be able to resubscribe any unsubscribed contacts manually from within your account, but unsubscribed contacts who want to return to your list can resubscribe themselves using a sign-up form.
Step-by-step guide taken from: http://support2.constantcontact.com/articles/FAQ/2073#oermission2