Let your users be part of a group and email communicate peer to peer without having to log into your Joomla site. Any mail send to the mailing list email address is forwarded to the rest of the members of the group.
You choose one email address, no matter if it is located at your own mailing server or at a free email service. The only prerequisite: it is possible to access the mails through one of the standard protocols POP or IMAP.
All recipients of the mailing list are defined in Joomla's backend - handy if most of your recipient have an user account (but they don't have to have one). Of coure you can also display sign-up forms on the frontend so that users can self-subscribe.
From now one your Joomla page will periodically check your private email address for new messages. If there are messages this message will be forwarded to all list recipients and stored for reference in your Joomla database. All your list participants have to do is use the one mailing address to reach everybody - no more manual maintenance of the recipients in their clients - the admin takes care.