On the page you can cerify if you have a mailbox and what are your CERN email addresses.
If you do not have a Mailbox you can create one by clicking on "Create CERN mailbox" in "Account Tasks" on https://cern.ch/account.
Your mail account will remain active as long as you have an active affiliation with CERN. When you leave CERN your CERN account will be blocked and then after 6 months will be deleted. If an external email address was specified for the account (on http://cern.ch/account) then the email routing for CERN email addresses will continue to work (messages will be forward to the external email address).