A small lever-device attached to a trombone. It is placed where the musician's support hand (the left hand for a righty) rests and holds up the instrument. The trigger increases the range of notes that a musician can play in one slide-position.
The thumb of the support hand hooks around the trigger, allowing it to be moved by slightly bending the thumb. When it is being used the trigger will change the notes played to those five positions down the slide (e.g., first position becomes sixth, second position becomes seventh.)
This allows a trombone player to fire off notes much faster than would be possible without a trigger. When playing an extremely fast or difficult progression this is a life-saver. However, it requires a certain level of skill to use the trigger. The musician will usually need to change his embouchure rapidly to play the new note, which can be hard at times.
Triggers cannot be attached to a trombone after it has been built-they must be part of the original design. If you're looking into purchasing one such instrument then you should seriously consider a model with a trigger.