Personal email addresses
Most often, each address is just an alias or redirect to whatever private mailbox the user has. Sometimes, however, they are true mailboxes (SMTP+POP3 or IMAP) with a certain space assigned.
Typically, addresses are used by a subset of members and staffers of Wikimedia entities, as needed or wanted for the respective activity. See Chapters email management for more information.
Only @wikimedia.org is consistently in use. Traditionally, the domain was used by volunteers who had shell access to change the relevant configuration file or convinced someone with access.
Every Toolserver user had a @toolserver.org email address named after their shell username. Similarly, every Wikimedia Labs tool has an email address in the form tools.<name>@tools.wmflabs.org, which is by definition not personal because any tool can be maintained by multiple users.
Users need to sign terms and conditions, then Wikimedia Deutschland usually checks their right to vote in Wikipedia and sets up their requested address, not with a postbox but as a forwarding to their own email. The service, which is gratefully accepted, is offered since 2011 and has not produced any bad experiences up to now.
For further information (in German) see w:de:Wikipedia:@.