I should point this out specifically I suppose, but it is mentioned other places.
Push mail has nothing to do with push notifications. Mail.app does not use push notifications, although there are many apps that are able to notify you on new mail, such as Boxcar, GmailPush, etc. Upon notification, then you can open your mail and get the latest messages.
To use push mail, you can
- Use Google's Exchange email service as described here (gmail.com accounts only) : http://bit.ly/4rEQSu
- Use the Mobile.me service which has a subscription fee.
You may only use one Exchange email account on the iPhone and it reduces battery life quite a bit. That's why notifications and manual fetching are better. Push mail is only needed if you really want to have all your new mail on your phone right when it is received.