In short, the catch-all email function allows you to receive all incoming email that is addressed to non-existent email boxes.
In your control panel email management tool you can setup POP, forwarding, and autoresponder email accounts which all possess unique usernames.
If someone sends email message to an email address that is not setup( or exists) as a POP, forward, or autoresponder, then the catch-all email function can forward these emails to an existing POP account which you specify. Therefore, you can "catch" all of the email that is sent to your domain name.
For example: A user may send emails to non-existent accounts if there is a typo in the username.
If the catch-all function is disabled, then any incoming email addressed to non-existent email accounts will be bounced back to the sender.
The catch-all function is an option which you can disable or enable. It is entirely your preference.
