iOS devices can be synced with an external server via CalDAV, CardDAV, and IMAP. How can I do the same with Android? Android out-of-box does not support CalDAV and CardDAV. ActiveSync is not an option as it's proprietary technology requiring costly licensing from MS.
I'm curious how Gmail itself syncs with Android. Are there any docs/examples (preferably, in PHP) which would let me implement a similar backend so that an Android device would be able to sync its mail, contacts and calendar with my own server?
Gmail, like most other apps on Android (Facebook, Calendar, Contacts etc) uses push notifications, in addition to the IMAP and POP3 protocols in case of mail clients.
You can setup GCM on your own server(s) through which you can send push notifications to your apps.