The simple answer
Push is the physical front end for Ableton Live. The pad grid is used for drums, melodies, clips and step sequencing. The encoders control devices, racks, mixer levels and macros. The display keeps key information in front of you so you can make decisions without staring at the laptop all the time.
Push does not replace Ableton Live. It changes how you interact with Live. The best way to think about it is this: Live is still the studio, but Push becomes the instrument you play to move ideas through that studio.