Found this on the www whilst googling around:
It's an update service for the factory Samsung apps that aren't available in the play store... S Voice, S Calender, S memo, messaging, any of the Samsung apps.... Prior to this there wasn't a reliable way of updating those apps without having Samsung Apps installed.... Even then it wasn't reliable... Now with this "Push" service updated Samsung will be able to PUSH out OTA updates to those apps if needed.... I am going to assume there is some sort of update coming to some of those apps which requires this service.... My money is on S voice... The S4 system dump showed up and that was a key improvement and I think they are going to push that version to the S3.... Again this is just my personal opinion and guess..... But I do KNOW that that is what the Samsung Push service is for... It is a more reliable way of making users aware of available updates...... Much like the Play Store and your carrier do....