Collecting enough lights (I think 10?) unlock the After Story. Yes, there is an animation showing that you grabbed the orb. Are you sure you did Misae's route immediately before doing the one you're doing right now (I think that's Tomoyo's route, if I remember correctly?), because if not, the choice won't even appear. Not all the time do you get the person's light in their route. Sometimes you get their light from someone else's route, or even the After Story.
Anyways, Yukine's route thoroughly explains what the lights are all about.