When we’re speaking about photography, reciprocity is the relationship between the ISO, aperture and shutter speed that ultimately forms the exposure. If we put it into a formula, it looks like this:
exposure = aperture x shutter speed x ISO
Basically, what this means is that if you reduce the aperture, you must also reduce the shutter speed. So, if you have a shutter speed of 1/250th, an ISO of 400 and an aperture of f/8 and your light intensity doubles, you must double the shutter speed and aperture to keep the same exposure. In this instance, your new settings would be f/16, ISO 800 and 1/500th. However, if you want your aperture or shutter speed to stay the same (for example to keep everything in the frame sharp or to freeze motion) then you must change one of the other two elements.
For example, if you have an aperture of f/22, a shutter speed of 1/125 and an ISO of 400 and your light intensity doubles (yet you still want to keep everything in the frame sharp), then instead of changing the aperture you must change the shutter speed and ISO.
However, sometimes at very low shutter speeds film can’t be relied upon to produce a good exposure. A few more stops of exposure are required to create an acceptable image. Reciprocity failure can also cause a shift in color on the film.