Your tickets are stored on your Uber account, but you'll need to display your ticket to board. If your phone is inoperable (e.g. your battery dies), you'll have to purchase a ticket another way.
If you uninstall and reinstall the Uber app or get a new phone, sign in to the Uber app to view your tickets.
A network connection is only required to purchase a ticket, which must be done before boarding. If you lose service after purchasing a ticket, you can still activate and display the ticket from "Your tickets" in the Uber app.