The wing increases attributes such as HP, DEF, Max ATK, min ATK etc. so that the CP will also increase. Wings will appear or appear when the star is max / becomes T1 or higher.
To get stars, wings must be upgraded using wing advancing pill. Wing advancing pills can be obtained from a field boss, gift code or from a pearl shop.
when the star is max it will increase its grade (to T1 T2 and so on), the wing will change its appearance and the attributes will also increase.
If I’m not mistaken, the Wing Feature unlocks at level 80,