PHPwebmail is a Web-based IMAP and SMTP mail client. Often it is not possible to make outside mail connections from networks behind strict firewalls, or to configure a regular mail client (for example in an Internet cafe).
With PHPwebmail a mail client only needs a WWW connection to the mailserver. Specifically it only needs a connection to the webserver hosting PHPwebmail.
Most of the times the Web and mail server will be the same machine but PHPwebmail can connect to other mailservers as well as long as an IMAP connection between these two machines is allowed.