With this device you can control the brightness of any incandescent lamp. A special semiconductor (called a TRIAC) is used to turn on and off the lamp very quickly. The more time it is turned on compared to off, the brighter the lamp is.
This picture shows the working principle of a TRIAC (source: www.electronics-tutorials.ws):
In the plastic case there is a 5V power supply, a microcontroller, and a high voltage board.
The high voltage board contains a TRIAC, an optotriac and an optoisolator for zero-crossing detection. (TRIAC: acts like a switch, optotriac: turns on the switch, optoisolator: detects when the wave begins)
The microcontroller receives the button presses from an infrared remote, and changes the lamp's brightness in 10% steps. Demonstration video: