Enlightenment is not yet available in global. It will be released some time early in 2019.
Enlightenment (called Kaigan in Japan) is a mechanic where a unit is able to progress beyond level 85 and gain a variety of benefits. To unlock the ability to obtain Enlightenment, you need to do spend a "Circle of Truth". These come in three colors: blue (for 1-3 star units), yellow (for 4 star units), and red (for 5 star units). For a five star unit, unlocking also requires 10 rainbow golems, 10 rainbow pots, 30 golems of the unit's elemental color, 30 Soul Alchemia, and 500,000 Zeni. This gives you access to the first gate (Envy). Each of the gates is named after one of the seven deadly sins, so while there are currently only three unlockable gates in Japan, the intention is that there will eventually be seven.
- Envy: Envy levels increase HP, PATK, MATK, and AGI. The capstone increases additional stats, differing by character. Requires LB 25, unit level 85.
- Sloth: Sloth levels increase PDEF, MDEF, CRIT, and Hit Rate. The capstone buffs one of the unit's passives. Requires J11 for the job of whichever passive it buffs. Requires Envy level 2.
- Lust: Lust levels increase HP, DEX, AGI, and Evasion. The capstone buffs the unit's leader skill. Requires Sloth level 2.
Each gate you unlock will also increase the unit's max level by +2, for a total of level 91 with three gates.
Leveling up the gates requires a variety of materials (you can review the full costs through the Japanese AlchemistCodeDB or through this Reddit thread), but in terms of soul shards, the first level in each gate takes 5 soul shards, then each level takes 5 more soul shards than the last. Level 5 is an exception, with a differing cost for each gate (30 for Envy, 50 for Sloth, and 40 for Lust). If you want to fully enlighten a unit ("5/5/5"), this will take 270 soul shards, but it's rare that you will do this. A lot of units run 4/2/3 (95 soul shards), 5/2/3 (125 soul shards), or 5/5/3 (210 soul shards). Here is a list of some recommended shard amounts for each unit (credit goes to Malyngnant).