A trigger-happy person is far too ready to shoot. The picture behind the word is a finger already resting on the trigger, waiting for any small excuse — a noise, a shadow, a person reaching into a pocket. It is not about being a good or bad shot; it is about shooting first and thinking afterwards. The word is always a criticism. You would use it about a soldier, a police officer, a guard, or a country that goes to war too easily, and you are saying they are dangerous — that people get killed who did not need to die.

Though actually, most of the time people say it about things that have nothing to do with guns. It has spread to mean 'too quick to do anything you cannot take back'. A boss who fires staff at the smallest mistake is trigger-happy. So is someone who deletes files, or bans people from a chat group, or sends an angry email at midnight. In tech, people say a system is trigger-happy when it sends alerts for problems that are not really problems. The gun is still in the word — that is why it sounds serious — but the real meaning has become 'acts too fast, and cannot undo it'.

It feels informal, a bit vivid, the kind of thing you say in conversation or read in a newspaper rather than write in a formal report. Note the hyphen: it is written trigger-happy, and it sits before a noun (a trigger-happy cop) or after 'be' (the guards are trigger-happy).