It has to do with with the turning force being applied to the head when tightening the screw/bolt/nut into position during assembly. Generally the higher the torque used to put the screw in, the better it will stay in position due to increased pressure on the threading. Putting too much pressure into turning the screw and you could damage the screw threading, the shaft threading, the screw head could snap off, you could strip the head, or damage the material you're fastening together.

So torque settings are recommended to both ensure the screw/bolt/lug will lock into place as tightly as possible, but not so tight that you will break something completely. The torque setting is determined by a variety of factors ranging from the materials being fastened, material of the screw, threading size, and physical size of both.

You set your tool to the torque setting. As you apply turning pressure with the tool it will hit that setting limit and click as the tool shifts/gives under the pressure. This is essentially the tool giving out before the screw does to ensure you don't over-torque and break something.

How well a screw stays in place is determined by threading size, original torque pressure, the material it's connected to, the environment, and other fastening additives like glue or locktite.