system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How do phones know you got a text, snapchat, etc... without soaking up a lot of data?

It seems like if they were constantly checking if you had a notification from any app it would use up a lot of data quickly.
gpt
Since this is really about power consumption, the answer is the phone turns off the radio. Basically it tells the cell phone it's going to turn off for a second, and if any data for the phone comes, it must be announced at exactly that second and the phone will power up it's radio and download the data. If no data comes it will immediately turn the radio back off. 

As for apps, internet connections over TCP support connecting and then waiting for transmissions so apps can use this to allow the phone to power off while connected. On Android many apps use this directly, but both Apple and Google offer push services that optimize this and put all the app notifications on one connection to reduce unnecessary wake ups. Apple actually forces this on their developers.