The concept is to run the LED at full current but for limited time. Instead of controlling the brightness by changing the current, you keep the current constant but flash the LED so rapidly that your vision can't see it, typically 200 times per second or faster. I normally use around 1,000 flashes per second for my applications. To change the brightness you keep the flash speed the same (the PWM frequency) but alter the duration of on time relative to off time (PWM duty cycle).
For example, if each PWM cycle lasted 1,000uS and it comprised 250uS with the current on and 750uS with the current off, the apparent brightness would be 25% of maximum. If it was 500uS on and 500uS off, th brightness would seem to be 50%.
Brian.