As the coolant gets hot, the hot water rises to the highest part of the system, out the top of the head and into the top of the radiator. Once the water is in the radiator it get a chance to cool down, so this relatively cool water falls to the bottom of the radiator, where it can then enter the motor again through a inlet pipe near the bottom of the barrel. This whole process causes the water to flow around the engine, thus cooling the motor.
This system works fine in an engine that is designed for it and is better than air cooling. However, it requires a larger capacity radiator, does not regulate temperature as accuratly as a system with a pump fitted, and is not as efficient as a pump system. Its just older technology, thats not to say it doesn't work well. It has just been superseded by more modern/better systems.
My toys 85 KXT250A2, 85 ATC250R, 85 Tri-z 250, 06 LT-R450, 04 YFZ450S, 07 125 typhoon x 3, 06 FPV GT.