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To understand more about what a publisher can do, we need to clarify about the Access Control Levels (ACL). In other words, ACL's govern the permissions that are associated with the individual User levels. There are seven (7) User Groups/levels within Joomla. Only Four (4) of which have access to the Site Front-end: Registered, Author, Editor, and Publisher. There are also three (3) levels with access to the Administrator Back-end: Manager, Administrator, and Super Administrator. In addition to the registered User Groups listed above, there is a Public (unregistered) or Guest, level.
So a publisher is a User level with access only to the Site Front-end functions, but with permission to publish content on the Site.