Reversibility of light simply means that when the path of light rays is reversed they follow the same path as when they were incident. In simpler terms, light rays will retrace the same path when reversed. It is the same as saying one uses the same route to go to school and come back from school.
There are numerous applications of reversibility of light. The most common application is the looking mirror that everyone uses to look at their own reflection. Looking mirrors use a reflective coating to ensure that light is reflected back, which we use to dress ourselves. Another application is the mirrors used by security guards to check under vehicles. Reversibility of light also allows us to see objects in clear water. This is also used in photography, where the light reflected back from an object is used to take a picture or make a video, that is why photographers sometimes use additional lights to get a better picture.
Hope this helps.