With Apple TV you can mirror your phone display onto your TV using AirPlay TV - Apple
More information on AirPlay and mirroring here AirPlay video from your iPhone, iPad, or iPod touch - Apple Support
Other devices like the chrome cast Chromecast - 2nd Generation - Google Store can be used to send some content to your TV. But only the Apple TV can mirror your entire screen onto the TV.
If you prefer directly connecting your device with a cable you can mirror your phone to your TV using this accessory made by Apple Lightning Digital AV Adapter - Lightning to HDMI - Apple