This item is an experience material.
To strengthen your girl by using this gem, It will cost :
Cost = n x ★ x 【 5 + ( level -1)】 CC
n = Number of Master gems
Example : Homura 4 ★ lvl 80
Using 2 Master Gems ---> Cost = 2 x 4 x 【 5 + ( level -1)】= 672 CC
It gives 150 exp.
This item is given as a reward for clearing some main story quest, and may also be obtained in the normal gacha.