When in the main menu (with the GTLife, Arcade, GT TV, Track Editor options available), after a certain amount of time, random demos will start to play. And I'm pretty sure they are random, ranging from day/night, weather, car types, dirt/asphalt, etc. You can't choose specifically what demo video you want to watch.
However, you can start the demo manually (instead of waiting for it to appear) if you press the circle button (and it will ask you if it can start the demonstration I think it's called).
And these "demo videos" have been around since the beginning of GT5 if I am remembering it correctly.