How can the Arduino Uno support up to 12 servos if it only has 6 digital PWM pins?
Although I haven't looked at the source myself, in these types of situations they usually use interrupt timer 1, which in PWM mode would have been associated with pins 9 and 10. This would explain why you can't use pulse width modulation on those pins. In fact, you can use any of the three timers for PWM on any digital pin, although it's not as good as the built in PWM options.


(source: bansky.net)

(Source)
The above image accurately describes how the signals are sent to the servo motor. Such a waveform is similar to a standard PWM. The servo library can translate a degree to a waveform that the servo's IC will be able to use to adjust the motor's position with it's motor and potentiometer.