Many principles remain constant when shifting from film photography to digital, and one characteristic that retains an analogue is that of image noise. According to the Merriam-Webster Online Dictionary, noise is “any sound that is undesired or interferes with one's hearing of something , an unwanted signal or a disturbance in an electronic device or instrument, or irrelevant or meaningless data or output occurring along with desired information”; in the case of image noise, all three definitions have a bearing on the topic.
Image noise is not all that different from noise in the audio realm; regardless of the type of camera, image noise is undesirable visual artifacts that are not a part of the original scene. Depending on the situation, noise can be a result of the conditions under which you’re shooting (as in the case of lens flare) or a result of your camera equipment. Often, noise is a function of both external and internal conditions. For instance, sensor size and pixel size play a role in noise levels - all else being equal, larger sensors will generally experience less noise due to signal than smaller ones, a fact that makes perfect sense when you consider that a larger sensor can get detect more photons and, thus, get a more accurate reading
With a film camera, increasing the ISO rating (the sensitivity of the film) or shooting under w light conditions makes it worse. In the case of digital photography, both high ISO and low shutter speeds tend to exacerbate image noise. Consider signal to noise ratio; the less light the photodetectors receive, the greater the likelihood that random fluctuations in light detection or the internal workings of the sensor will introduce noise into your image.
One way to manage the noise (if you’re using a digital SLR) is to use a faster lens or, if possible, shoot at a wider aperture. Greater light gathering ability will help to tilt the signal-to-noise ratio in your favor. Another means of coping with the problem is to use image processing algorithms (either in-camera or using a personal computer) to filter out the noise. The problem with this approach is that legitimate data can be mistaken for noise, too!