As of v1.66.0 there are seven elements in the game which are Fire, Ice, Storm, Normal, Magic, Spirit, and Hard. Fire, Ice, Storm and Normal are associated with both monsters and attacks, Magic is associated only with attacks, and Spirit and Hard are associated only with monsters. Before factors like elemental resistance or spell piercing are factored in, the elements interact like so:
So, when a fire attack is used on an ice element target the attack deals 30% more damage than usual (130%). If a fire attack is used on a fire element target the attack deals 80% less damage than usual (20%). Any other combination of single element attack versus single element target will deal damage as shown on the table above.
Many attacks have two elements. As examples, Fireball is both Magic element and Fire element, Blizzard is both Magic and Ice element, StormTap is both Magic and Storm element, and so on. However, only the non-Magic element on such attacks will influence damage output, so in effect the table above applies to these attacks as well.
Double element attacks such as a physical attack with an elemental enchant, though, will result in damage output based on a combination of how both elements interact with the target's element. As an example, an attack from a player with five points in fire enchant will deal roughly 110% as much damage to an Ice element target as it would to a Storm or Normal element target; that same attack would deal roughly 75% as much damage to a Fire element target as it would to a Storm or Normal element target.