Chromecast does not display the device's content. It allows you to use a windows/Mac/Android/iOS device to find content that then streams to your TV via the internet. At it's most extreme, it replicates an entire Chrome tab on-screen. It is not a peer-to-peer device, nor is it mirroring the device's display.
Basically, you can have a party with a YouTube jukebox, and everyone who attends can use their own phones to find the next video for the queue.