Google does a great explanation:
Example: Ben is Mary’s personal assistant. Ben often needs to send email on behalf of Mary, and he uses Send mail as to send emails for Mary from her [email protected] account using his [email protected] account. Because Ben and Mary email each other often, it’s confusing for Ben to see his emails to Mary appear as unread in his Inbox. Also, when Ben composes a reply to Mary’s email, the To: field shows his primary email address
In this case, Ben should turn off the default Treat as an alias setting. With Treat as an alias turned off, Ben’s emails to Mary will appear in his Sent mail and not in his Inbox, and when he composes a reply to Mary’s email, the To: field will show Mary’s primary email address.