In a bicycle air pump, a reversible valve refers to a valve that is suitable for both types of bicycle valves: the Schrader valve (typically used in car valves) and the Presta valve (the narrower valve often found on road and mountain bikes).
You can switch between the two valve types by changing the inside of the pump head. To do this, unscrew the cap and turn the inside upside down. Then screw the cap back on.