Mats (MP in French) means raw material.
It can be drilling elements, cut up (looted during a hunt) or OP mats (which arrive in the GH, when it has a Outpost) or you can buy them to Merchants (in dapper, in Elyps, and/or Guild points). You can even receive gifts (on events) or when playing to the Wheel of fortune.
You can store, sell them (using forum, or to merchants, Black Market...), or craft them to make clothes, jewels, weapons, tools...
There's different level and type: since Patch 00837 (December 2020) stars show if it's basic (no star), fine (1 star), choice (2 stars), excellent (3) or Supreme (4).
