Refer to figure. 
The balance tab is an aerodynamic device to assist the pilot in moving the control surfaces. The figure shows a balance tab fitted to an elevator.

For aircraft with fully mechanical controls, control forces can sometimes become quite heavy at high speeds as the dynamic pressure increases. The balance tab is designed to deflect in a way that aerodynamic forces help the pilot to move the main surface (in this case, an elevator). A balance tab moves in the opposite direction of the control surface, as this pushes the trailing edge of the elevator in the direction we want it to go, for the small price of sacrificing a small amount of elevator effectiveness. 

For instance, if we want to pull up, the elevator needs to deflect upwards so the small balance tab will deflect downwards in order to assist the much larger elevator to travel upwards.

The tab is usually connected via a linkage, and moves with the control surface. So the pilot directly controls the control surface which moves the tab through the linkage mechanism. 

You may have seen this during a preflight of an aircraft fitted with a balance tab, when moving the elevators, the balance tab will travel in a direction opposite to the movement of the elevator.

A disadvantage of balance tabs is that they reduce control effectiveness slightly, as they apply forces in the opposite direction to what is being commanded.