A curse prevents you from removing an equpped item. I suspect the Daemon's Curse effect randomly curses a piece of its victim's equipment.

Curse are easily broken however. They can be removed either through the priest spell "break curse" or at the Item Shop for a price.

The Daemon's Curse trap causes the affected character to lose a point of VIT. I was wondering about it, so I opened one.

A Daemon's Curse trap has two confirmed effects. The first is a -1 penalty to Vitality. Secondly it lowers the character's "energy," a hidden score heavily influencing how stats are adjusted when you level up.

Daemon's Curse is generally considered the inverse of Goddess Judgment, which raises the player's energy and should never be disarmed. Simply open a Goddess Judgment trap to undo accidental Daemon's Curse damage. A charge from a Hardy Ring's special ability will give a character a point of Vitality as well, so while Daemon's Curse sounds bad, it's very easy to repair the damage.