What does awakening equipment do?

When equipment items have reached their max level, they can be awakened using Secret Books of Refinement and other necessary materials. Awakening equipment increases its ★ count and raises its max level. Awakening can also unlock an extra ability for some items.
The max levels for equipment items are listed below.
Equipment item max levels:
★: Lv. 10
★★: Lv. 20
★★★: Lv. 30
★★★★: Lv. 40
★★★★★: Lv. 50
*There may be some exceptions.