That has nothing to do with how or when ships take damage. It only determines the minimum level of damage indicated on the HUD necessary to fail the mission.
There is a full explanation in the Mission Editor tutorial:
Damage threshold is the minimum % damage that will cause the mission to fail. If you
leave it at the default of -1, the mission will not fail simply due to any damage to a player
ship—however, damage below the waterline can still cause a player ship to sink, and
that will terminate the mission in failure.
Damage inflicted via a damage_engine trigger will still affect speed or steering and may
make it impossible to finish the mission.
For all but the simplest arcade style missions, you should set a positive Damage
threshold just high enough to allow leaving some paint on the dock.