^^^ What Pete said ^^^
Especially important when inviting others to a calendar event, yes?
Make the calendar event and select invitees.
Go to Settings > email + accounts > tap the account name associated with the calendar and make sure calendar is set to sync (box checked). Hit the back button... Anytime you make a calendar entry you want synced to other devices or invites sent make the calendar entry... Then go to Settings > email + accounts > hold down on the account name associated with the calendar and tap "sync" from the popup menu. You have now manually synced that calendar across your devices and pushed notification out to invitees.