It means, the card can provide better visual experience (both in audio and video) while watching Blu-ray movies that come with 7.1 Channel audio when connected through HDMI.. You can notice well in games than in movies.. If HDMI supports only 5.1 Ch and you play a 7.1 Audio, you'll get only a 5.1 Ch sound effects only.. Take a look at this..
You select any one as the audio output device and that's where the audio goes.
And no, you cannot experience 7.1 Ch in a ordinary headphone/headset, you need a 7.1 Ch headset/headphone (google it and see) for 7.1Ch sound effects..
A very good sound card will offer better sound effects than the port in the GPU..