From Dragon Quest Wiki

LoveRain (Rain of Amor in Japanese) is a healing ability that first appeared in Dragon Quest Monsters 2.

It also makes an appearance in the PS1 and 3DS remakes of the first two Monsters games. Learning it requires the monster to reach Level 21 with 116 HP, 96 MP, 78 Agility and 263 Intelligence. It is naturally learned by the BigEye, Brushead and MimeSlime. It can also be learned by monsters with Meditate and LifeSong.

Its Japanese name may be a reference to the item Amor seco essence (known as Amor water in Japanese - note this item also appears in the Monsters games with the translation of "LoveWater").