There are 3 types of damage in the game: Normal, Fantastic, and True. Basic attacks deal normal damage. You will encounter some enemies who are resistant or even immune to a specific type of damage. To defeat those enemies, you'll need to review their description to see what they are immune to, and then find a team of Heroes that inflicts the damage type that will hurt the enemy.
Each Hero has detailed stats on the Hero screen. If you're looking for more information tap the information icon next to the Hero's name.