To provide the mailing lists functionality to your customers, you need to install and (in case of Plesk for Linux) configure the corresponding component. The mailing lists support is included in new Plesk installations by default. If it is missing from your server, you can add it using the Plesk Installer. Look for the Mail Hosting > Mailman component on Linux, or the MailEnable mail server component on Windows.
In Plesk for Linux, you need to configure the mailing list component before the mailing lists functionality can be provided to customers. To do so, go to Tools & Settings > Set Up Mailing Lists Server (found in the Mail section) and specify the mailing list administrator's email and password. After you set up the mailing list administrator's account, the Set Up Mailing Lists Server option will disappear. Afterwards you can configure the mailing list software or change your administrative username and password by browsing http://lists.<your Plesk server hostname>/mailman/admin/mailman.
It is important to note that to use the mailing lists functionality, you need to add “localhost” to the mail server's white list. To do so, go to Tools & Settings > Mail Server Settings, open the White List tab and add 127.0.0.1 to the white list. However, this will make it impossible to use outgoing mail control. If you need to both use outgoing mail control and provide the mailing lists functionality to your customers, you can suggest that your customers use mail forwarding instead.