The Xbox One Controller can be independently upgraded to increase functionality. The process is fairly simple, but does require a physical connection to the Xbox One. First, connect to Xbox Live. If you're planning on using a Stereo Headset Adapter with the Xbox One, plug it into the controller, and also plug the headset into the adapter.
At this point, the update may begin automatically. If it doesn't, press Menu on your controller and select Settings. Go to the System sub-menu. Select Controller Update.
The update should begin, and should only take a few minutes. If you run into an error, hold down the console's Xbox button for five seconds, wait a minute, power back on, and try the update again.
The update is not currently mandatory.