Cursed is an ability from Unique monsters. Players hit by such monsters have a 50% chance of being cursed with Amplify Damage, identical to its Necromancer counterpart. Taking any damage from such monsters can inflict the curse, including from the Charged Bolts released by Lightning Enchanted monsters, the Frost Nova released by Cold Enchanted monsters, and the Holy Fire/Freeze/Shock of Aura Enchanted monsters.
When the curse takes effect on a player or a player's Hireling or summoned pets, the player, Hireling, and pets are all cursed if they are close enough to the monster, putting entire parties at risk of being cursed.
Cursed is a very deadly unique attribute, and Cursed uniques should always be approached with caution.