You can start watching a broadcast on one device, and transition to watching it on another. Simply ensure both are running iOS 8+ or OS X, have Bluetooth turned on, and are logged in to the same iCloud account.
To log into your iCloud account:
On OS X - System Preferences -> iCloud
On iOS - Settings -> iCloud
Handoff is great for when you’re using our web view to watch a broadcast on your Desktop, and want to quickly switch to watching on your iOS device (or vice versa).