A "standard" computer fan has two pins; one for power, one for ground. A three-pin fan adds an additional pin used for the signal from the hall-effect sensor. A speed-controlled fan generally uses a four-pin connector, and is commonly referred to as a "PWM" fan.
It is my understanding that any DC motor can be driven with PWM instead of a steady signal, so I am confused why there is a need for an additional pin for the PWM signal. Is the PWM signal fed into a MOSFET or some similar switching component on the fan itself in order to control the speed of the fan?