Reincarnation offers a way to re-grow your unit, with a chance for overall higher stats.
The Japanese wiki uses a formula to determine good or bad growth. Essentially, (Current STATS - Base Lv 1 STATS) divide (Current Level - 1). That will give you the average points gained per level on your unit.
Based on the above, gauges are 2.5 (Bad), 3.0 (Avg), 3.5 (Good), 4.0 (Excellent).
You can check your unit base stats at Lv 1 in the reincarnation screen.
You will require the reincarnation unit (from medal shop generally) to do a reincarnation.
Unit level will reset to Lv 1 on reincarnation.
Pimped stats from fusion are retained on reincarnation.
Limit break is retained on reincarnation.
Skills levels are retained on reincarnation.
Weapon proficiency is retained on reincarnation.