Essences are stats that you drop into empty slots on certain pieces of armour. They allow you to focus on the stats that are important to you. The lotro-wiki has an excellent write-up (although the example pieces are mostly from level 105 -- 120 armour doesn't have that many slots!) so I won't duplicate that, but I did write up a condensed version of where to find the T12 essences for putting into level 120 gear.
A quick note: once slotted, essences will be destroyed or sold WITH that piece of gear, unless you use an Essence Reclamation Scroll. These can be bartered for at the skirmish camp, and a variety of other places, as described in the link above.
Lotro-wiki Essence Post
Grey Mountains - T11 & 12 Essences
The best essences in the game right now are tier 12. You can tell an essence is tier 12 because it has a small number twelve in the upper left-hand corner. The numbers in the bottom right-hand corner are NOT the tier -- they show how many of that essence you have in that stack.
There are 3 types of essences available in the Grey Mountains (ranked here lowest stats to highest):
A) Weak Mithrin Essences: yellow title, T11, item-level 366
B) Mithrin Essences: purple title, T12, item-level 372
C) Empowered Mithrin Essences: purple title, T12, item-level 378
Wiki Essence Index
All 3 are available at the Adventurer's Quartermaster in Skarhald.
The Empowered Mithrin Essences can also be crafted. The recipe is auto-bestowed to any crafter with the Ironfold tier open.