It's the "inheritor" of the galactic mantle.
It's pretty much what the trilogy is about. The humans, forerunners, and possibly elites are fighting over the true inheritor of the galactic mantle and the galaxy.
The definition: To receive (property or a title, for example) from ancestors by legal succession or will. What it means in Halo: Reach; It's a hexagon with a comet on it with stars. The symbol represents the rank being top notch (you can't get higher because you already reached the stars).