Tabs are a way to reduce the amount of stick force (i.e. force applied by the pilot) required to deflect a control surface in a mechanically linked system. In most modern aircraft hydraulic or electric systems fill the same purpose

To give a simplified explanation, a small tab located at the trailing edge of the surface is deflected by the control linkage. The deflection of the tab generates an aerodynamic force which then creates a moment around the control surface hinge, moving the entire surface.

So if you deflect the tab upwards, that air flow over the tab generates a downwards force that acts to move the control surface down.