Disc Two is only available in the Legendary Edition. This one is a standard DVD, rather than an Xbox 360 disc; you can play it in any DVD player. The material on it is oriented towards the hardcore fan - this is stuff that's really aimed at folks who want more from their Halo experience, who want to get to know Bungie just a little bit better. Let's look at the specifics, shall we?
Halo and Halo 2 Cinematics
One of the loudest complaints heard about Halo 2 was 'pop-in' - the graphics glitch that caused cinematics to begin with no textures, with actual content 'popping in' visibly after a second or two, as the Xbox struggled to keep up with the heavy memory demand. This was an unfortunate side effect of Bungie's decision to remove loading screens in Halo 2 - but it bothered people... it bothered them a lot. Bungie has taken great care, then, to re-render these cutscenes to avoid almost all graphical glitches; you can see them exactly the way they were intended to be seen. (Even better, in some cases; a bit of post-processing work was done to ensure that you get the best experience the Halo engine could provide.) The Halo 1 cutscenes didn't suffer from texture popping - but these, too, have been re-rendered, and are as clean as they've ever been.
