Digital noise in photos taken with digital cameras is random pixels scattered all over the photo. It is a similar effect as grain in film photography and it degrades the photo quality.
Digital noise usually occurs when you take low light photos (such as night photos or indoor dark scenes) or you use very slow shutter speeds or very high sensitivity modes.
When taking pictures with a digital camera an electronic sensor (also known as a CCD) built from many tiny pixels is used to measure the light for each pixel. The result is a matrix of pixels that represent the photo.
As with any other electronic sensor the CCD is not perfect and includes some noise (also know as white noise to hint on its randomness attribute). In most lighting the light is significantly stronger than the noise. However in extreme scenes where the light is very low or when a high amplification is needed noise levels can become significant and result in pixels in the photos that include more noise data than real photo light data. Those pixels usually appear as random dots or stains on the photo (for example white dots scattered randomly on the photo).
Understanding digital noise in various scenes:
low light (night photos or dark scenes): when the scene is dark the amount of light measured by each pixel of the CCD is low. When the light intensity is very low it can become too close to the level of noise naturally found in the CCD. In such cases some pixels can appear as noise because the noise level measured for them is significantly close or higher than the actual light intensity.
slow shutter speeds: when the shutter is kept open for a long time more noise will be introduced to the photo. A slow shutter speed translates to the CCD integrating more light per pixel. The effect can be easily understood as the CCD accumulating light in each pixel and measuring the total light over the shutter period of time. However at the same time the CCD is also accumulating noise. For that reason in slow shutter speed photos some pixels will appear as noise because for these pixels the amount of noise integrated is significantly close to or higher than the actual light measured.
high sensitivity modes: high sensitivity in digital photography is implemented by mechanisms that result in amplification. The CCD amplifies the measurements it takes. However there is no way to just amplify the actual photo light that falls on the CCD pixels instead the noise and the actual light are both amplified. The result is that the CCD becomes sensitive not only to light but also to its own noise. When too much amplification is applied some pixels will appear as noise.
While it is impossible to completely prevent digital noise there are a few options that allow you to significantly decrease it. When taking photos in low light scenarios such as night photos there are two main parameters to play with: sensitivity and shutter speed. Raising sensitivity creates more internal noise in the CCD while slowing down the shutter allows for more noise to integrate on the CCD. The amount of noise generated by both parameters is different. It is recommended that you set your camera to manual mode and play with a few different sensitivity/shutter speed pairs to find out the one that generates the least noise.
Some cameras include a built-in feature called noise reduction. Noise reduction is implemented by sophisticated software that can identify the noise pixels and remove them. For example the software can identify the noise pixels based on their randomness and usually extreme intensity gap between them and their neighboring pixels. Removing the noise can be implemented by interpolating a replacement pixel value based on its neighboring pixels.
If you do not have a built-in noise reduction feature or it does not work properly you can use a PC based software that removes digital noise. Many photo processing software include a combination of automatic and manual digital noise removal. Some software packages can also use a few photos of the same object to average them and thus remove the noise (relying on the fact that digital noise is random and the noise pixels will be different in each photo taken).
To conclude digital noise should be understood by any amateur or professional photographer. However for most photographers digital noise is not a practical problem even in low light scenarios usually digital noise is minimal and can be significantly reduced by simply turning on your cameras noise reduction feature. For professional photographers who shoot in more extreme conditions digital noise can present a real problem and can be dealt with using a combination of optimizing the camera settings and removing noise with professional software.