First, what do you mean by "app"? Do you mean a native hybrid app, like using PhoneGap/Cordova?
I don't see PHP (or any server language) as very useful for a reminder app. It might play a minimal role, by providing a place to store reminder data and perhaps share it between devices. Of course, this would be duplicating the reminder apps that nearly everybody already has built-in to their phones and tablets.
It wouldn't make much sense to have PHP do the "reminding". That should be done locally. Yes, you could use a websocket or polling, but it just doesn't make sense to maintain a connection to do something that is best done locally.
You might use PHP and a database to store the reminders, and sync to a device or devices.
But you might also just use localstorage, a SQLite database in PhoneGap, etc. And iOS (and I presume Android) apps can back-up their data (e.g. the SQLite database) to iCloud, etc.