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the more pressure you put on the water, the closer the molecules become... (could you make ice this way... ) and the more heat the water is able to contain untill it gets to the rad and is cooled again... or so it seems.
That's pretty much it. Boiling point at 1 Bar is 100 C, 2 Bar 120 C, 20 Bar 212 C. and above 221.2 Bar (3210 PSI) there is no such thing as liquid/gas phase water. Since you pressurise the system, it can run hotter. Since the efficiency of a radiator is proportional to the difference between the hot and cold sides, running at higher pressure will let you run hotter and so use a smaller radiator.
The other point that is so obvious it is easily missed is that hotter fluid carries more energy per unit mass/volume. This means that running hotter not only reduces the radiator area needed, but it also allows the coolant to carry more energy per unit volume - reducing the size of the cooling system needed.