A stationary front is simply a front that is not moving. It is represented by alternating blue and red lines with blue triangles pointing towards the warmer air and red semicircles pointing towards the colder air.
Weather conditions greatly depend upon which side of the front a location is positioned. If a stationary front is nearby and a low pressure center is approaching along the front, heavy amounts of precipitation are possible.
Image by: WXP Purdue
There is usually a noticeable change in temperature and wind shift crossing from one side of a stationary front to the other. Low pressure centers sometimes migrate along stationary fronts, dumping heavy amounts of precipitation in their path. Such a scenario has been depicted above. The alternating red and blue line is the stationary front and the blue and green swatches indicate precipitation.