Send agent replies to ticket creator via email.
Create new ticket from incoming emails that can't be matched to existing tickets.
Create a reply to existing ticket from incoming emails, if email is in reply to that ticket.
Having all three of the above options enabled will essentially turn the site into a shared inbox. All incoming and outgoing emails will be converted into tickets and replies.
Send a notification to user, if their ticket has not been created, because ticket creation via email is disabled.
Send a notification to user via email informing them that their ticket has been received.