If you’re using the latest Apple devices and all your software is up to date, then your iPhone will now use Bluetooth to search for nearby AppleTVs as well as just searching on the network using Bonjour. The end result is the same – streaming over the local Wi-Fi network – but if you have an odd or non-standard Wi-Fi setup, this might help[,your devices talk to one another.
I sometimes don’t see AirPlay speakers listed on my iPad, and I have a single router setup with just two networks running on there. If you use multiple subnets you might never have your iPhone see your Apple TV.
Now, with iOS 7.1 and Apple TV 6.1, the devices can talk to each other direct over Bluetooth 4 and then work out the Wi-Fi part between themselves later.
According to AFP548, the requirements are as follows:
Apple TV with version 6.1 (released 3/10/14)
iOS device with version 7.1 (released 3/10/14)
IP connectivity between the two devices
Bluetooth 4.0 compatible devices
Who needs NFC, right?