You get them from knocking out crystal wyverns and they can be used to get a better tame from a crystal wyvern. They are just better than crystals but be warned! They will spoil in 45 min. Don't start harvesting them until you find the one you want to tame and make sure to put them in a fridge but not in a tamed crystal wyverns inventory as they find this a delicious snack.

They can be gathered by knocking out wild Crystal Wyvern or their Heir counterpart and pressing the use key (E by default on PC) to harvest the crystals from their bodies while unconscious. Another way to harvest Primal Crystals, although is not recommended due to its difficulty, is to kill an Alpha Blood Wyvern.