You can only activate this card when an effect that inflicts damage to your Life Points is activated (except Battle Damage). Negate the Effect Damage you receive and your opponent then selects 1 card from his/her hand and discards it.
Man, why do people get stuff like this wrong so often? Mask of the Accursed's effect DOES start a chain (and you could use something like Energy Absorbing Monolith on it). The issue here is that Trap of Board Eraser's fail card text is fail. It (like most Counter Traps) can only be chained to a Spell/Trap activation, not the activation of a Spell/Trap effect.
First, cards are bounded by the rules. No cards could be activated against continuous effects.
Continuous effects are effects that statisfy these conditions:
1. Need no player activation (can be triggered however)
2. The effect remains when the card stays on the field (or graveyard, some cases)
Continuous effects cannot be chained (thus cannot counter, but you can counter when the card first activates).
Harpie Lady 1/2/3 - This card is always treated as "Harpie Lady"
Unhappy Girl - Cannot be destroyed by battle, opponent's monster cannot change position
Burning Land - 500LP every standby phase
Skull Invitation - 300LP every card sent to graveyard
Note that continuous spell/traps might not be continuous effect:
Beast Rising - You choose to activate it
The Japanese version is slightly different, if we try reordering the sentence:
This card can only be activated when a monster effect or spell/trap CARD inflicting damage to your LP is activated.
As you may see...this card counters the activation of a card, or monster effect.
For character abilities...they are overriding the rules already. They cannot be countered, nor negated. (You can special summon Labyrinth Wall with Paradox Brothers' skill even dueling Vagabond with challenge forbidding special summons.)