SLF,
The minima is a statutory requirement. For example ( Cat 3b approach) the measured and reported visibility must be 75 metres or more to commence the final segment of the approach ( say the last 4 miles) the Decision height ( also part of the minima) is the height by which either the required visual reference is aquired or a go around MUST be initiated. In the case of the example I have given that visual reference may be as little as "One centreline runway light". The higher the minima the more lights that must be visible.
The simple reason for this is that the Pilot must be able to manually complete the landing in the event of failure of the automatic systems. In the case of a manual approach the Pilot must be able to correct drift etc and maintain enough visual guidance to complete the landing.
The formulae for calculating the various minima is fairly complex in that takes many factors into account. "Minima" provides a very simple definition for the Pilot to make a safe decision in this regard.