There are four elemental types in ROM: Fire, Water, Wind, and Earth, and characters can apply elemental attack and elemental resistance stats in several ways, such as through equipment, collection effects, etc.  Monsters also have elemental attacks alike characters, and you can check the attack element of monsters that appear in each region on the [World Map] → [NPC & Monsters] tab.

The element found in a monster's information means its primary attack element, and increasing the same elemental resistance stat in a battle with that monster can reduce the damage it takes from attacks.

In addition, each of your character's element attack stats is applied when attacking an opponent, and damage can be partially reduced depending on the opponent's element resistance, so knowing the monster's attack element and preparing the corresponding element resistance stats before you go into battle can help ensure a smooth battle.