Maybe this explanation might help:
Normal bulbs work by putting a voltage across the bulbs' contacts. This causes a current to flow through the thin wire (filament) in the bulb. The filament then gets hot and glows emitting light. The higher the current, the brighter the bulb, but too much current and the bulb goes pop. Dimming the bulb is possible by reducing the current flowing through the bulb, this can be done by using a variable resistor. Typically on the end of the small knob you turn which dims the lights.
LEDs work differently, they are basically either on or off. Though if you put too much current through them they also go pop. So to dim a LED you turn it on and off very quickly. If you do it quickly enough the eye doesn't realise that the LED is flashing. The longer the time the LED is on compared to the time the LED is off, the brighter the LED appears. To give you an idea of how quickly - the duration of the individual on and off times may be in the order of hundred'ths or thousand'ths of a second. To do this you need some sort of electronic circuit - the scope of which is beyond this (hopefully) simple explanation.
Hope this helps,
- tenpin