what does it mean push on iphone

It means rather than checking for mail every 15 minutes or so automatically (fetch) or opening the mail app to manually get your mail (also fetch) new mail will be sent (pushed) to your phone every time a new one is available. You will hear a mail alert noise and notice the badge on mail has incremented by 1.

oh my bad

Do you mean with reference to email notifications?

With Push set to On - you will be notified of a new email almost instantly when the email arrives on the server. You do not have to launch the mail app to see when new emails arrive. This can apply to apps as well. The information is instantly available by way of a notification rather than having to launch the app to see the information .... News apps use push notifications for real time updates.