I don't know how it is on Android but on iOS for example, you can make phone calls only the Phone app. For example, the Yelp app gives you the business info and when you tap the phone number it switches to the Phone app. For the most part, that's fine but having an SDK like Twilio allows you to keep the phone calls and the user inside your app.

That can be pretty interesting in terms of user experience where your user stays in the same context instead of switching back-and-forth between your app and the Phone app.

VOIP for games is the most obvious. I imagine someone can build out a "Say Something" competitor to Draw Something pretty easily using this API.

The ability to answer calls within your app. You can build call-aware mobile apps that know who's calling, and present relevant information to the user.

Cleverly, I've got a prototype app that does just that with the Twilio Client for iOS - I don't think the Twilio part was more than 10 lines of code :)

The ability to integrate VoIP that uses the data connection instead of the voice network into apps.