SquirrelMail is capable of retrieving e-mail from a POP3 server, via the included Mail Fetch plugin. However, SquirrelMail requires an IMAP server to run atop of. The IMAP server store the e-mails and is also used for authentication, so if there is no IMAP server, SquirrelMail can not be used.
The difference between IMAP and POP3 is that the IMAP protocol store e-mails on a server, and the POP3 protocol is used to retrieve messages from a server, storing them locally in the client used to access the e-mail account. SquirrelMail, as most (if not all) web mail applications, is designed to give an end user access to his/hers e-mail regardless of location. Obviously, moving (downloading) the e-mails from a server to a particular computer would defeat this purpose.
Many ISPs allow access to e-mail accounts through both the IMAP and POP3 protocols (check with the ISP for details). If an end user wants to access an account using both an IMAP client, such as SquirrelMail, and a POP3 client, the POP3 client must be configured to leave all e-mails at the server, only storing copies of them locally. There usually is a "leave e-mails on server" (or similar) option in the POP3 client configuration.