Yes.... probably an exchange server* where the mails are kept on the server and your computers and phone just access your mailbox on the server. Derek is using his ISPs mail server via POP3 which is a protocol that downloads the mails onto the first device that connects and then deletes the mails from the server by default.
*you might not have an exchange server, which is Microsofts email server. other mail servers support IMAP instead of POP3, which also works the same way as your's does.