Calendaring is a great example. At least it's possible to get a unified view of my work Exchange calendar and my Google personal calendar, as well as manage both through the web, Siri, or any number of apps on every platform.
That's not possible without an open application protocol. I can't get a similar unified view of my Twitter and Instagram follows, for example.
JSON-API[0] for example, is layered on top of HTTP and an open protocol.
[0] http://jsonapi.org