Fire – Sets enemies on fire. Enemies who are on fire take damage over time.
Ice – Freezes enemies. Makes enemies brittle, taking extra damage from physical and ice sources of damage.
Stone – Not a damage type, stoned enemies, like frozen enemies, take bonus damage from physical, however not from ice. You can have a stoned AND frozen enemy for combos but the damage modifier wont be any better.
Physical – Base type of damage.
Lightning – Electrifies enemies. Upon death, electrified enemies explode doing damage in a small radius.
Arcane – Arcane damage debuffs enemy allowing them to take a flat additional amount of damage based on the damaging trap, to include the same or other arcane traps.
Acid – Causes enemies to take damage over time.
Some enemies also resist / take less damage from some sources.