They don't mirror your mail, you receive a pushed mail on the msgpush account telling you new mail has arrived.
You still have to read it on your regular account
Yes, "something else" the iPhone supports in OS 3.0, which is "push notifications".
These is a background notification service any iPhone app can use that can show a text message on the screen and update a counter (aka "badge") on the icon of an app that isn't running.
Push notification in iPhone OS 3.x is not to be confused with Exchange or ActiveSync so-called Push email.