: I'm an ignoramus trying to understand what the advantages of this are
: exactly. Obviously the textures are the same, so is it that the models are
: all less pixelated and so appear smoother? And this lets you see things in
: more detail further away?

Downsampling smooths all the jaggies and aliasing of the geometry. Think about it this way--while textures have real sizes in pixels, geometry is just math, it can be rendered as "large" as you want. It would probably be a more dramatic difference on a newer game than Halo CE though--given that it was deliberately designed to be low-poly friendly.