What does ISO stand for in digital cameras?

ISO stands for "International Organization for Standardization".  ISO has replaced the older ASA designation.

Since digital cameras do not use film but use image sensors instead, the ISO equivalent is usually given.
What ISO denotes is how sensitive the image sensor is to the amount of light present. The higher the ISO, the more sensitive the image sensor and therefore the possibility to take pictures in low-light situations.



ISO Speed & Exposure
ISO speed affects the shutter speed / aperture combinations you can use to obtain correct exposure.
Suppose your digital camera's light meter warns you there is not enough light to correctly expose a scene. You could use the on-board flash, but let's suppose again it's not allowed (like in a concert or indoors recital).
You would then need to use a higher ISO. Set on "ISO Auto" mode, your digital camera will automatically select a higher ISO. Otherwise, you can manually select the next higher ISO and see if the increased sensitivity allows you to obtain a correctly exposed picture. If it does, you can now take a correctly exposed picture.
Similarly, if you find the camera is using a shutter speed that is too slow (1/60 sec. and slower) to handhold the camera steady and shake-free (thus resulting in blurred pictures), and you cannot open up the aperture anymore, and you do not have a tripod or other means to hold the camera steady, and you want to capture the action, etc. etc. -- then you might select the next higher ISO which will then allow you to select a faster shutter speed.

ISO Speed & Noise
However, all this increase in sensitivity does not come free. There is a price to pay with your image appearing more noisy.
See, when you boost the sensitivity of your image sensor by selecting a higher ISO, the image sensor is now able to record a fainter light signal. However, it is also true now that it will record fainter noise, where noise is any signal that is not attributed to the light from your subject. Remember that an image sensor is still an analog device and it generates its own noise, too! The increased sensitivity allows the image sensor to record more light signal and more noise. The ratio of light signal to noise (S/N ratio) determines the "noise" in your resultant image.
An image sensor is usually calibrated so that it gives the best image quality (greatest S/N ratio) at its lowest possible ISO speed. For most consumer digital cameras, this value will be expressed as ISO 50, ISO 64 or ISO 100. A few digital cameras use ISO 200 as their lowest ISO speed.
Just as with its film counterpart, an image sensor will exhibit "noise" (comparable to "graininess" in film) at the higher ISO speeds. Unlike film, where graininess can sometimes contribute to the mood of the image, noise produced by an image sensor is undesirable and appears as a motley of distracting coloured dots on your image.