Enlightenment 2 means you can use 2 insights that could affect you. They can be 2 of the same if they come from different sources and have an additive (+1) modifier. You cannot use the effect from the same model twice, nor would you benefit from two of teh same enlightments that do not have an additive.
IE: Red Demon with enlightenment 2 is hanging out with a bunch of Legionnaires and 2 Keepers. Assuming he has an ally in base contact, he could benefit from Guard twice, because it grants Guard (+1) and there are 2 sources of the insight. Now, a Shield of Taeflon comes under attack and the Red Demon and his cronies rush to his aide. On later rounds, the Red Demon comes under fire and can now chose the Spirit Fire Insight as one of his 2 enlightment options. He would not want to chose the Spirit Fire option twice (assuming there was more than 1 Shield around) because having 2 wouldn't grant twice the backlash.