Leadership XP is somewhat like AA, except it goes with your regular (and AA) exp. Group and raid leaders can work on their leadership XP by leading a group or a raid into battle. Like AA, you can stock up on pts for innate group abilities, which you can see by pressing "L" by default.
Don't expect to see much result until after many hours of leading a hunting or adventure group, for it looks like the leadership exp bar is equivalent to a regular 40s+ exp bar.