Dark frame subtraction is a noise reduction technique for digital photography. Here's the premise:
For short exposure (less than a couple seconds, let's say), the noise of a digital camera's sensor is acceptable. But as exposure times lengthen beyond that, the noise gets amplified along with the subject of the image.
So if you take an exposure that's 15 seconds long, you'll record 15 seconds'-worth of noise along with the subject matter you're photographing.
However, it's also generally true that sensors are noisy in predictable ways. Some areas of the sensor are usually noisier than others, which means that if you know where the noise is, you can use some fancy math to get rid of it. And the way to do that is: Dark Frame Subtraction.
You take your normal picture, and then you take a 'dark frame,' which is where you put the lens cap on and take an equally long exposure. The idea of the dark frame is to gather the noise without any subject matter. In our 15 second example, you'd take the picture you want, and then take another 15 second picture of the back of the lens cap. You then combine these two images in an image editing program, like Photoshop, in the subtraction or difference blend mode. Alter the opacity of the dark frame to suit your tastes.
And voila! Magically the noise is reduced, if not eliminated.
Many digital cameras include a dark frame noise reduction feature. This is usually what the 'noise reduction' setting involves.