When an image is scanned into a computer, it is done in a specific range of colours. For instance, a 32-bit image has a higher range of colours than a 24-bit image, which again has a higher range of colours than an 8-bit image and so on.
Bradley (1993) states the problem as follows.
Let's say you want to display an image that has n colours. However, you can only get m colours, where m<n. Thus, somehow you must choose which colours to use. This process is known as Colour Quantisation.
It is a process that must be done `correctly'. That is, correct to the viewer's eye. For example, let's say you want to look at a lovely GIF image of a lady in a bright blue bikini. In quantising the colour, the GIF viewer chooses its range of colours as all blues. While the bikini will be represented as realistically as possible, the poor lady's skin would be shaded in various tones of bright blue, along with her hair, the trees in the background and the sand on the beach. Thus, the GIF viewer would do well to choose what could be described as `important' colours - some skin tones, some hair tones, some sandy tones and some blue tones for the swimsuit.