One of the new features that has been added in Exchange 2016 and Office365 in OWA is a birthday calendar which is a dedicated calendar for the Birthday appointments that are associated with contacts. eg Like many of the special folders in a Mailbox the folder name for this is localized so if your mailbox is set to use a different language this folder name should appear in your localized language. Unlike most of the special folders in Exchange there is no WellKnownFolder enumeration for the birthday calendar so if you want to open this folder you either need to search for it by name (as long as you know the localization of the Mailbox) or you can use the following extended property that should exist on the root mailbox folder. So in EWS you can do something like the following to access the HexEntryId value from this extended property which you can then convert to a EWSId using the ConvertId operation and then you will be able to bind to the folder...
Pushing the Envelope in Messaging and Office 365 Development