The fully CGI cinematic was first aired at the opening ceremony at BlizzCon 2011. This is not the name of the cinematic in the full game, and this version is slightly-edited (to remove some plot info) from the full version.
It's not known where this cinematic will be seen in Diablo III -- perhaps after Act Two, as it introduces Azmodan who is the end boss for Act Three. (If not earlier, as foreshadowing for the upcoming events.)
Cinematic Content
The cinematic begins with Leah, who is lost in thought while reading Cain's Journals. She falls into a trance and is transported (mentally, not physically?) into the Burning Hells, where she receives a menacing lecture from Azmodan, before he gives her a preview of the demonic invasion he's launched, through the crater of Mount Arreat.
As this is an edited version of the cinematic, we do not know if it ends differently in the full game, or how literally to take the events seen in it. View it below.
The transcript of Azmodan's speech:
Cinematic Stills
A selection of images taken from this cinematic. Many more can be seen in the Black Soulstone image gallery.