When the assignee posts reply in the ticket, the customer will get an email for that. Now, the customer can click on the default 'reply' button on the email and write down the reply with attachments in the email itself. That reply will be automatically updated in the relevant ticket within a few minutes. So customer doesn't need to log in into his account everytime to solve his issue.
That reply will be received on the email id specified in gateway settings (for ex. firstname.lastname@example.org). That reply will be updated in the ticket only if that email is kept unread.
Similarly, the ticket can be automatically created when an email is received at the specific email address. (for email@example.com)
You just need to setup an email gateway and the Magento cron to synchronize the tickets with email.