How does PopCorn Time iOS installer work?
In Xcode 7 (beta), Apple has released free iOS provisioning profiles for all: https://developer.apple.com/library/prerelease/ios/documentation/DeveloperTools/Conceptual/WhatsNewXcode/Articles/xcode_7_0.html

Which means you can now install arbitrary iOS applications through a computer onto an iOS device without having to purchase a license from Apple, without having it to be approved by Apple, and without needing specific provisioning profiles installed on the device.

I'm guessing they're just using this to their advantage.