They aren't push notifications, but client-side notifications that respond to the user's learned habits and situation. I guess some of Google Now's functionality could be offloaded to push, but lots of it is based on the user's location, which isn't available on iOS to an app that isn't open.
User location is available to background iOS applications; Apple includes two APIs specifically for that purpose: fine and course background location updates. The app will be notified whenever the user's location changes, if it's activated or not.
I thought that only worked for apps that were once opened (since the phone last closed) and hadn't yet been killed by iOS's background task management thing?
