This is just one-time configuration step where the user has to provide the email address, password, and some server configuration information.
It is very hard to track the communication done with particular candidates through emails, as everyone uses their own email address. Email sync make the process smoother by centralizing all email communication at one place and allow you to see the complete conversation history.
Mailbox allows Admin and Manager to view all the emails sent by their coworkers to different candidates or clients. This can be used when a manager or owner wish to see what email sent by the team to different clients and candidates. In this case no need to open individual mailbox of team member but just team mailbox.