'Hey Cortana' is the name of a new feature for Windows Phone 8.1.1 tied to the Lumia Denim update. It was announced in September 2014 during Microsoft's Berlin event for the new Lumia 730 and Lumia 830.
Hey Cortana is also a marquee feature in Windows 10 for PC, which launched in July 2015 and Windows 10 Mobile. The feature will also be coming to the Xbox One later in 2015 when it receives Windows 10 as well.
For mobile, Hey Cortana makes use of SensorCore and the Qualcomm Snapdragon 80x series chipset to bring passive-voice listening to the Cortana personal assistant. A more simplified explanation is users can say 'Hey, Cortana' to wake up their Windows Phone, enabling Cortana to take commands for inquiries, requests or actions.
Because Hey Cortana requires SensorCore and the Snapdragon 80x chipset, currently only the Lumia 930, Lumia Icon, and Lumia 1520 support the technology. Newer phones like the Lumia 950 and Lumia 950 XL also support the feature. Those phones need the corresponding Lumia Denim firmware to enable the feature. Hey, Cortana is a system app, meaning once it is on the device, it can be dynamically updated through the Store by Microsoft.
Users train Hey Cortana by repeating 'Hey, Cortana' four times in a quiet room. User voice clips are stored locally to ensure privacy and users can reset the training at any time. Hey, Cortana is also optional, as the user can enable or disable the feature through system settings.
For PC, the process is the same as modern computers can also have passive listening enabled. Although it does consume a small amount of battery most users will not notice and it is ideal for desktop PCs who are always connected.