"Push" is a general term that refers to technologies that allow a central system (such as the mobile phone network) to send ("push") information spontaneously and quickly to an end-user (perhaps via their mobile device), without action on the part of the user or mobile device.
Email is a good example of a technology that can be "push" - or not - on a mobile device.
With push email, emails are "pushed" directly to the mobile device as soon as the email server receives them.
Email is not "push" if the user has to manually check for new email, or if the mobile device has to check the server for new email at regular intervals.
SMS (text messaging) is inherently a "push" technology.
Mobile web (WAP) content can also be pushed to mobile devices, although this is not as common.