Touch lamps work by activating an internal electrical switch when the capacitance from the lamp meets the capacitance from the human body. The circuits within the lamp detect the change of capacitance when someone touches the lamp.
The electrical switch for a touch lamp is internal instead of external like other lamps. That switch is connected to a circuit that is wired into the part of the lamp that is touched for power. The capacitance of the lamp, or the lamp's capacity to hold electrical charge, is calculated so that the capacitance of the human body is also required to activate the switch. Once the hand is removed from the external layer of the lamp, the lamp's capacitance returns to its regular charge.
Some touch lamps have the ability to glow brighter or dimmer if the lamp is touched multiple times. These lamps are set on a particular dim setting. The light from the bulb is cycled on and off several times a second, but it appears to be a consistent brightness to any observer. When the light is at its brightest, the bulb is receiving the maximum amount of power it receives in a normal lamp. This eliminates the need for a three-way light bulb.