Noise is often defined as any deviation from a "pure" signal. The signal is taken to be brightness pattern of the image so any variation in the pixel values that represent the image is noise. These variations arise principally due to:
Shot noise. The random way photons are emitted from a lightsource causes random variations in image brightness. The fewer photons you have the more this noise is evident. Can be reduced by getting more light onto the sensor.
Dark current (thermal) noise. Heat produced by the camera (which being electromagnetic radiation just like light can show up on the sensor). Since it's not part of the scene it's noise. It can be reduced by cooling the sensor, limiting exposure times (the longer the sensor is active for the more it heats up) or shooting a dark frame (i.e. with the shutter closed or lens cap on) to subtract from the original image (some cameras have a setting to automate this).
Photo response non uniformity (fixed pattern noise). This arises from imperfections in the silicon that cause pixels to be slightly more or less sensitive than their neighbours. Calibration can reduce PRNU, although it can be dependent on parameters such as exposure time.
Read noise. Electrical noise that is generated by the circuitry which reads the values from the sensor pixels. Can be reduced by using a higher ISO (in the case where the signal is not maximised, amplifying the signal prior to readout means read noise is a smaller percentage of the signal) or using a camera with lower read noise. You can look at the shadow noise figures at base ISO to give you an idea of read noise.
Quantisation noise. Rounding errors when an analogue signal is converted into a finite set of descrete digital values. Not usually noticeable, can be reduced by using a sensor which stores more bits per pixel e.g. 14 instead of 12.
The following are technically noise but rarely referred to as such:
Moire/aliasing. A sort of spatial quantisation noise, aliasing arises due to interference patterns and the fixed spacing of sensor elements. It can be reduced by an anti-aliasing filter (usually fitted to the sensor as standard) or increasing the sampling frequency (number of pixels per unit area) i.e. more megapixels with the same lens.
Compression artefacts, when an image is stored as a JPEG. Can be reduced by selecting the highest quality setting for JPEGs or shooting raw.
Hot pixels, stuck pixels, dark pixels. Sensor elements that always give either zero or the maximum possible response.
The term "colour noise" describes how the noise manifests itself - it's not a source of noise like the above. Colour noise refers to random variations in the colour of pixels, not just in their brightness. Colour noise is easy to remove since the eye is less sensitive to spatial variations in colour, the loss of detail due to noise reduction is less noticeable.
Again "high frequency noise" refers to another characteristic, the spatial frequency, or how close together the peaks of the noise are.
