Film Speed (ISO)
Film speed is a leftover term from film photography, which is now applied to digital photography. It is more commonly refered to as "ISO".
"ISO" is the International Standards Organisation, which organises worldwide consistent standards like this, but everyone still just refers to film speed as "ISO" anyway.
What is film speed?
Film speed refers to how sensitive the film or sensor is to light. The higher the number, the more effect light will have. In film photography, this would be achieved by using film of a different chemical composition, but it is achieved by electronic amplification in a digital camera.
Film speed is usually written as ISO followed by a number, e.g. "ISO 100" or "ISO 400". In fact, my digital camera has a button labelled "ISO", despite it being the wrong term, technically speaking.
Importance of film speed
Consider you want to have a fixed shutter speed and aperture (for example you want a certain depth of field or there are some other restrictions) but the exposure is still too low. What can you do? You can amplify the light electronically by increasing the ISO: ISO 200 will make the sensor more sensitive to light than ISO 100, increasing the exposure of your photo.
This is how ISO fits into exposure. It gives us one final element of control over the exposure of a photo. It is also the least often used - consider it a last resort. Let me explain why...
Dangers of a high ISO - noise
It's tempting to just increase the ISO value quite high to make taking photos in low light conditions easier. But remember that this is an electronic amplification - gain. Increasing gain in electronic circuits always introduces something called noise - unwanted random signals.
I won't cover noise here, but as a rough rule of thumb, don't exceed ISO 400 if you want to blow up your photos, as you may begin to see unacceptable levels of noise. Generally leave it as low as the camera allows as much as possible, especially during a bright day.