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