Regeneration is a buff that heals the character's health at the end of the turn. "End of turn" will not be evaluated if you win the battle - if you kill the final enemy, Regeneration will not trigger.
Regeneration works similar to 
Poison. The number represents the amount it will heal and the turns left. After each turn, the number decreases by one. When the number reaches 0, Regeneration wears off.
Because of its linear decay per turn, multiple 
Regen Potions stack quadratically: taking one can restore 15 HP over 5 turns (5 + 4 + 3 + 2 + 1 HP), but taking two in succession and starting off with 10 Regeneration can restore drastically more than that in the first two turns (10 + 9 + 8 + ... + 1 for a total of 55 HP over 10 turns). It can be improved even further with the assistance of 
Sacred Bark
Sources of Regeneration
Regen Potion: Gives the player 5 Regeneration (10 with Sacred Bark)
Notes
- Not to be confused with the Awakened One's or buffed elite's Regenerate ability, which heals at a flat rate at the end of every turn without decaying.