Welcome to the forum.
Did you watch the video demo on a computer, or only on a mobile device? If only on a mobile, you may want to watch again on a computer. The video includes annotations that answer many of the questions you're asking above. Unfortunately, annotations don't display on youtube if you're watching on a mobile device.
VoxCommando is communicating with the VeraLite using the Vera plugin for VoxCommando:
http://voxcommando.com/mediawiki/index.php?title=Plugin_VeraAs per the video annotations, there is a specially developed Android app for VoxCommando called VoxWav:
http://voxwav.wikispaces.com/VoxWav+HomeThe remote control device is the Amulet from Amulet devices:
http://www.amuletdevices.com/The voice is coming from the Windows computer that is running VoxCommando (albeit through stereo speakers). This is known as text-to-speech (TTS). Windows machines typically come with a couple TTS voices, but it's also possible to buy voices, some of which are much more natural-sounding than the built-in voices. In VoxCommando, one can tell the computer to issue TTS announcements in response to specific commands.
If you're new to home automation, building a system that does what is demonstrated in the video is probably something to aspire to, rather than something to try to accomplish right off the bat. But maybe some other folks here can recommend a good place to start.
