Destroy
The elimination of a game piece (Invaders, Dahan, Spirit Presence, Island Boards, Spirit) by dealing Damage equivalent to the piece's Health. Some effects also destroy pieces regardless of Damage or Health. The Destroyed pieces are generally returned to the supply.
Not to be confused with Remove, which deals no damage and simply takes the piece off the board and returns it to supply, and Replace which deals no damage and changes the piece into a different one. [Base Game: p. 13, 15, 18]
Invaders
Destroying a Town 
generates 1 Fear 
, and destroying a City 
generates 2 Fear .
To destroy an Invader, you must deal Damage that meets or exceeds its Health in one turn. Some effects also destroy Invaders regardless of Damage or Health. [Base Game: p. 15]
Dahan
Every 2 points of Damage destroys one Dahan 
, because they have 2 Health each. If an effect deals Damage to Dahan , it can be dispersed to any number of in the affected land(s), which may end up destroying zero Dahan .
Spirit Presence
Adding Blight 
to a land destroys one Presence from each Spirit in that land.
Destroyed Presence is removed from play (set next to the Island), not returned to the Spirit Panels! (If it was returned to the Spirit Panel you would have to cover something revealed on a presence track, greatly reducing your power in the game).
Some effects can restore destroyed Presence. [Base Game: p. 13]
Spirit
If a Spirit loses all their Presence on the Island, that Spirit is destroyed and players immediately lose. [Base Game: p. 13]
In the rare case that a single Power Card or other effect causes you to both win and lose, you win a sacrifice victory: you are destroyed, but the island, the Dahan, and many other Spirits survive. [Base Game: p. 12]
Island Board
The Island Board and everything on it is removed from play. See Cast Down Into the Briny Deep.