Apple's current implementation of AirPlay, its media streaming technology, requires a Mac or iOS device to be on the same Wi-Fi network as an AirPlay receiver, which in most scenarios is the Apple TV. While seamless, AirPlay in its current form makes it impossible to use in places where you don't have access to a local Wi-Fi network.
Feeling your pain, Apple in iOS 8 has implemented zero-configuration peer-to-peer networking between AirPlay devices. This lets you broadcast whatever content from an iPhone, iPod touch or iPad to your Apple TV, even if these devices are not on the same local network...