Said of firearms, a hair trigger is is the trigger of a weapon adjusted to release with the application of very little force; that is to say a gun that requires little pressure on the trigger to fire. The term is from a trigger so adjusted so that one must only move it a "hair's breadth" to fire the weapon.
This term is also employed as a description of many other unrelated things, and is generally used to describe a tense person or volatile situation that only requires a small movement to combust.