Push email is what the blackberry is renowned for.
The blackberry enterprise server will push a new mail when it arrives to your phone, likewise microsoft have active sync for exchange server which will push new mail as it arrives to your iphone.
Pushing email to a mobile device will result in the mail arriving on your phone/pda almost the same time it hits your enterprise mail server. The advantage is you dont have to get your phone to poll the mail server every few minutes which will consume the battery on the mobile device.