The short answer is, black backgrounds are created as a result of a 5 ‘stop’ difference in exposure levels between the main subject and its background.
The long answer is : Your camera is unable to see as well as the human eye.
This is one of the reasons, why we sometimes get very contrasty images with ‘blown’ highlights in light areas and very dark shadow in other areas.
Our eyes can see up to 16 different levels (or in camera terms ‘f stops’) of light, which means we can differentiate between very light areas and very dark areas and still see detail in both.
The camera however, can only make-out a 5-6 different levels or ‘f stops’ of light. The way it over comes this short fall, is to combine very dark areas and very light areas into one block which either come out as jet black, or pure white, and do not contain any other information or detail.
This shows up as clipping on your camera’s histogram. If the image is under exposed or has too many dark areas it sends the histogram off to the left. Over exposure, or too many light areas sends the histogram off to the right.
Black background are created when the area behind the main subject is more than 5 stops darker, so the camera groups them all together and they come out as jet black on the image.
If you would like to try this for yourself, find a nice bright subject with a dark background. For example a white flower in sunshine with a dark green evergreen leaf as a background, preferably in shade.
If your camera has spot metering, use this to take an exposure reading off the flower.
Compose the shot with the flower in sun and the foliage behind it in shade and you should find the image comes out with a nicely exposed image of the white flower with the dark background foliage being too dark for the camera to see and therefore appearing black.
If you don’t have spot metering on your camera, the other way to do it is to switch your metering to manual.
I took this fall leaf (see above) in autumn sunshine by walking up to it and manually setting the exposure in the camera. I then took a few steps back and recomposed the shot with the leaf as the main subject, but pointed the camera at a shady area behind and took the photo.
This as you can see resulted on a nice bright well exposed leaf with a dark background with one or two highlights visible.
My only regret is that the right hand leaf was damaged and I didn’t spot its imperfection, till I got home and studied the image more closely on the computer.