ISO is effectively a sensitivity of the sensor, whether it be film or digital. In theory, ISO for a digital camera should be the same as for a film camera.
The ISO on film is determined by the grain size of the chemical. What this will mean is that the resolution will be better with a lower ISO film. Also, because a film grain is all or nothing, this will lead to some spottiness, or noise.
The way that ISO is achieved in a digital camera can help to understand why it is important, and why using a higher ISO isn't always a good thing. I don't know the way it was achieved in film, so I can't really speak to it, but I imagine it's using somewhat similar principals.
First of all, Matt did an excellent job explaining the different sources of noise. What happens in a camera actually comes down to the following.
- Light hits the sensor.
- The signal on the sensor is passed through a gain circuit. The amount of gain depends on the ISO setting being used.
- The signal value is then ran through an A2D converter. What this will do is map the amplified signal into a range from 0 to 255 (Or higher, depending on the number of bits in the converter), a digital signal.
The camera then may remove some of the basic sources of noise, especially the "Dark current" noise. That's the signal if you were to expose complete blackness.
So what actually happens when you turn up the ISO? There's basically two paths, which I'll cover below.
If the ISO is increased, and the shutter speed correspondingly decreased, then the signal level going into the A2D converter remains the same. However, the amount of signal on the sensor is decreased. That means that any noise which is sensor depended will in effect be amplified. This includes things such as Shot Noise. Some other forms of noise won't be amplified.
The second option is if the original image was underexposed, but the ISO brings it to being correctly exposed. It is possible to contrast enhance the underexposed image to have the same max/min as the correctly exposed image. The signal coming out of the A2D converter will effectively have a smaller range. This will leave only a few light levels, leading to a much noisier looking image than the correctly exposed image.
A few other interesting things. Sensors tend to bleed if they are saturated to neighboring pixels. If an image is increased in ISO and decreased in shutter speed, then it will not be saturated on the FPA itself, removing some artifacts. This can lead to somewhat better performance when saturated.
In general, high ISO on a digital camera will have less noise then the same ISO on film, due to a much better way to achieve high ISO.
Hopefully this wasn't too technical, but I'm just excited to share my knowledge of Electrical Engineering with the community:-) Let me know if you have any more questions, and I'll try and explain it even better.
To answer the second question, I'd say that lower ISO isn't always better, but in general, it's best to use the lowest ISO you can. If you are shooting indoors, for example, a higher ISO will allow you to use a shorter exposure time, leading to less motion blur. Usually I use the lowest ISO that will allow me to not be over the hand-limit of 1/lens_length shutter speed. But there are always exceptions.
