3-pin fans have a positive pin (where the fan gets power from), ground pin (negative pin), and tachometer pin (tells you how fast it's turning).
The idea is that the fan runs at full speed when you have 12 volts on the positive pin, but if you apply 7 volts to the pin instead, the fan turns slower. If you lower the voltage enough, the fan will eventually stop. This normally occurs around 4-6 volts. All of this occurs on the positive pin.
This is about the extent of how most people think of voltage control, but there's an entire world of confusion when you start talking about HOW the controller goes from 12 volts to 7 volts. This is very important when you start talking about water pumps or magnetic bearings (Corsair ML Pro fans).
If I've answered your question at this point, you can ignore what follows. It gets pretty hairy.
In order to control the voltage that the fan is running at, the controller does not actually generate a 7 volt signal. It actually can't, as that requires some really expensive parts. Instead, it turns the power to the fan on and off very quickly. It uses the ratio between on and off (called duty cycle) to vary the amount of power that the fan gets. This is called PWM, and it is used on the power pin of the 3-pin fan when you set it up to be "voltage controlled". Confused yet? So was I. It turns out that the only difference between 3-pin and 4-pin fans is that in the 3-pin fan, the PWM signal is combined with the power signal, and it is separated to the 4th pin of a 4-pin fan. A 4-pin fan must recombine the PWM control signal back into the power signal in order for speed control to work. The advantage of the 4-pin design is that the fan's control circuits can still have power even when the motor is in "off" mode from the PWM signal.
There are many reasons that they treat 3 and 4 pin fans differently. For example, for magnetic bearings, you need power for the bearing at all times. Turning the power to the fan on and off (3-pin) would also turn the bearing on and off. That's bad. In a 4-pin setup, though, the PWM signal is separate from the power, allowing the bearing to stay on even as the motor switches on and off.
Another advantage of the 4-pin approach is that you have power for the fan's circuitry at all times. In the 3-pin setup, the fan's circuits effectively have to "reboot" each time you turn them back on. This means that in the 4-pin design, you can switch everything at a frequency that people can't hear. In a 3-pin design, you have to switch at a much lower frequency and often generate audible noise as a result.
Sorry if that was confusing, but this entire subject is rather complicated. There are many more details that play into how speed control works, but I tried to limit this post to the parts that are important for most people.