In simple terms reciprocity is the relationship between aperture and shutter-speed.
Film or electronic light sensors are designed to be very sensitive to light and therefore the light must be controlled in order to avoid over-exposure.
A camera controls the amount of light from reaching the sensitive film or sensor by the aperture in the lens and the shutter-speed in the camera body. The aperture controls the light intensity and the shutter-speed controls duration.
The wider the aperture; so allowing greater more light intensity to expose the film or sensor the shorter time the film or sensor can be exposed to the light, before we have a problem with over-exposure.
A simple analogy for reciprocity is making toast: Toast can be made on a high heat for a short time to get a perfect brown finish or toasted at a lower heat for a longer period of time to obtain the same result.
Substitute the idea of toast for film or sensor and consider the light acting just like the heat. The brighter / more intense the light the shorter the exposure time required and the dimmer the light the longer the exposure time will be required to obtain the same results.
A practice example in photography, the camera set to ISO 100 a shutter-speed (sec = seconds) of 1/30sec, f/5.6 (10 EV) will produce the same exposure as 1/60sec, f/4, (10 EV) the same as 1/125sec, f/2.8 (10 EV) the same as 1/250sec, f/2 (10 EV)
As the aperture opens wider; so the shutter time must shorten to compensate. These combinations can be charted on a table and allocated a single number to described all the same exposure values. All the above combinations are known as 10 EV on an exposure-value (EV) table (based on an ISO 100).
To sum up, reciprocity can offer the photographer a number of combined aperture and shutter setting to achieve the same exposure. The choice however, may be based upon a required depth of field or a need for speed to capture a specific moment. There is an inevitable trade off, one for the other, a smaller depth of field will require a larger aperture and thus a faster shutter-speed. A smaller aperture for a greater depth of field requires a slower shutter speed. These combinations can be referred to as an exposure value (EV) number. This is the basic rule of reciprocity.
Basics Photography 07, Exposure. By David Prakel. Published by AVA Publishing