Definition of a Trigger Spring:
A trigger spring is placed behind the trigger of a firearm so that when the trigger is pulled, it'll return to it's original position once the user releases the trigger.
Due to various firearm designs over the years, there are many types of trigger springs as there are various types of triggers as well. Some may be compression, torsion, or double torsion springs. Usually, when it comes to compression trigger springs, there is a hammer which pushes up on the trigger spring when the trigger is pulled; so once the trigger is let go of, the spring pushes back on the hammer, causing the trigger to return to it's original position.
To the right, you will see some examples of various trigger springs.