To expand upon this, the basic circuit used in the modern triac dimmer is fairly simple in its basic form.
The triac is a semiconductor device which will conduct only after a suitable trigger voltage has been applied to its gate terminal. It then continues to conduct until the through current drops to zero, which of course will occur at the end of each half cycle.
The resistance of the dimmer control is placed in series with a capacitor so that adjusting the control alters the rate at which the cap will charge on each half cycle. The voltage across the capacitor is then used to trigger the triac into conduction (via another semiconductor device known as a diac).
Thus as the resistance is increased, the capacitor takes longer to charge each time and the triac is triggered into conduction at a later part of the half-cycle.
You can find many links to dimmer notes and circuits here: http://www.epanorama.net/links/lights.html#dimmer