Noise is most commonly found when using high ISO speeds such as ISO 800 and above. As the sensors sensitivity is increased by turning the 'gain' up dots start to appear in the picture, mainly in shadow areas first, then across the whole picture. The higher you push it the more intense the dots become, and the less usuable your picture becomes.
Noise also occurs when editing a picture. If you push the exposure to far, or push fill lighting too far this 'digital grain' will start to appear.
For example, tune your TV into a frequency that is unoccupied by any broadcast channel. The random fuzzy dots that you see on the screen are the work of "noise". Similarly on your DSLR or PNS camera, noise is unavoidable. Imagine those fuzzy dots slightly embedded onto your pictures and becomes more apparant as you increase your ISO from 100 all the way to 1600. Hope this gives you a good picture of the term "noise" =)
Some background on relationship of ISO, Aperture and Shutter Speed.
Its like an amplifier in your home HiFi system. It takes a small signal and blows it up. Similarly on your camera, light falls on your CCD/CMOS sensors and build up electrical charges, how fast this charge builds up depends on the intensity of light falling on it. Your ISO setting is an amplification to your sensor readings. The larger the ISO value the larger the amplification factor and "brighter" the captured image would be.
Its like a window to your room, the larger you open it the more light falls into your room but light gets more dispersed. As you gradually close the window, the light rays get gradually concentrated. This parameter affects your Depth-Of-Field (DOF). Wider your aperture and more light enters, you'll get smaller the DOF a "brighter" image.
This is how long you allow light to build up the charge on the CCD/CMOS sensor. The longer the duration allowed, the more the charge builds up and the brighter the image becomes.
To increase shutter speed, you need to increase ISO, open up the aperture or both. When you lower ISO in low light conditions, you probably end up needing a longer exposure duration (slower shutter speed) and thus the inability to freeze moving subjects. However, you get images with lower noise. Although noise may still be apparant but it won't be as significant as a shot taken at high ISO. Reason for this is that noise is suppose to be random, they are distributed evenly throughout the duration of exposure. For the case of ISO, a high ISO value will amplify the readings on the sensor, not forgeting that noise would be amplified with the same factor too.
Simply to say, you want a harmony between the 3 parameters. Give and take. Hope this helps.
Thanks for the lead Fragnatic and putting it into layman terms Override2Zion.... need to absorb and appreciate the relation between the trinity. I've been these reading these 3 terms very often, reckon they form the foundation of good photography theory... the rest is practise.
Noise removal stuff like Noise Ninja. Or some filters in Photoshop. But ultimately this isn't perfect. Useful details will be removed along with the noise, so the image will appear less sharp. Because it is very difficult for the software to figure out what's useful details and what's useless details (noise). That's why super high ISO is sort of like the last resort, when aperture, shutter and flash already maxed out.
You're welcomed L-plate. Yeah i agree with hvpdmg about noise removal. A great plugin for photoshop would be Noise Ninja, relatively easy to use. You can remove noise off a picture substantially but you'll end up with a softer image.