Apple introduced Passbook with iOS 6.0 as a way to store all your tickets, coupons, boarding passes, loyalty programs, and other cards all in one place. You would expect that since it was an Apple product, it would be proprietary, but it seems that Microsoft has somehow been able to add Passbook support to Windows Phone 8.1.
The Passbook passes themselves are a collection of code which are rendered and displayed by Apple's Passbook app. Microsoft has managed to recognize this code so that the Wallet app can now render it for you. Since Apple usually code-signs their Passbook cards, and it's not yet clear if Microsoft is simply accepting Apple certificates or accepting any pass regardless of whether it's signed or not.
Apple also provides a push-notification-based service to update cards, like gates numbers on boarding passes or balance info on Starbucks cards. Its not clear how Microsoft handles this at this time as the notifications would have to be Microsoft-specific support from the supplier.
In a perfect world a system like Passbook would be universal and everyone could use and benefit from it no matter who manufactured their device or built their operating system. That's how we get standards and standards is how we get mass market adoption.
We know that Apple is working with Microsoft to use Bing as their official search engine for Siri, so we assume there may be an official agreement between the two on Passbook support. If not we expect Apple to put a stop to Passbook support on Windows Phone when they find out about it, technically or legally.