As per my understanding it is user who has access to publish the specific page/resource.
Documentation goes like this:
Depending on the environment, the agent will use this user account to:
collect and package the content from the author environment
create and write the content on the publish environment
Leave this field empty to use the system user account (the account defined in sling as the administrator user; by default this is admin).
means this replication agent comes into action only when replicating the content from packagemenager(by clicking replicate for specific package) ? or activating the page/resource from siteadmin?