If you use multiple Google calendars and want to sync them all to your Apple iOS device, Google tells you go to http://m.google.com and change the settings there.
That doesn’t work.
What you need to do is head to http://m.google.com/sync on your iOS device and from there you will get the proper screen to choose your device and check the Google Calendars you want on your device. Easy.
You can also try www.google.com/calendar/iphoneselect if all else fails.