Frontal positions on weather maps show where the boundary touches the surface of the Earth. The boundary can be thousands of feet above the ground a couple of hundred miles away from the surface front. If there's enough humidity in the air, clouds and precipitation will form as warm air overruns cool air along a stationary front. Sometimes, stationary fronts can stay stationary or nearly so for days. When this happens, the sky can stay gray with rain or snow.
Stationary fronts are also good places for new low pressure areas to begin and grow into storms.
All about stationary fronts on the University of Illinois Web site has a little more information about stationary fronts.