The basis behind a scale system can be best explained with reference to 2D games (3D games inherently have some scale system). For example, imagine a program which moves a sprite object left or right when the controller is pressed.
The most intuitive way to do this would be to alter the sprite's screen co-ordinate by 1 pixel for each movement iteration. Alternatively, implementing a scaling system would allow you to move the sprite by fractions of pixels. Instead of the sprite's co-ordinates being represented in screen co-ordinates (eg. a value of 0-319), the scaled representation values would be much larger than this (eg. a value of 0-{319*4096}, where 4096 is the scale factor). The scaled value is only converted to a screen co-ordinate at the screen control level (i.e. the sprite co-ordinate is set as the scale co-ordinate divided by the scale factor). At all other times, the scale co-ordinate is the only manipulated variable.
Choosing a representation like this presents flexibility which may be harnessed in a number of ways.
The implementation of scale systems is partially necessary to compensate for the lack of floating point maths (i.e. fractional) in the Playstation. However, it is likely that scale systems will be a faster alternative to floating point maths for most hardware.