The clickers for finger shooters is normally a little metal wire that rests against your arrow. As you draw back with fingers and anchor it is still sitting right near the tip of the arrow.
As you start to execute your shot and pull hard against the wall, the arrow moves back about 1/16-1/8" and the clicker falls off the end of the arrow. This is what causes the click and signals the shooter to release the arrow.
A lot of good shooters use these. However, I don't shoot fingers, I shoot release. When I have experimented shooting fingers, I could not shoot a clicker. My mind would say, the pin is not in the middle do not release even though the clicker clicked.
It is supposed to be a form of target panic reducer. Hoperfully some other finger shooters will pop in here and can provide more advice