Dimming is accomplished through SCR (Silicon-Controlled Rectifier), IGBT, or sinewave dimming systems.
Dimmers are controlled by a low voltage signal from the light console. In older systems this signal is analog (AMX or Analog MultiPlex). Since the late 80's the signal is is a digital protocol (DMX or Digital MultiPlex). Many newer systems are using Ethernet to control dimmers. In response to one of these signals, dimmers allow power to flow at the specified level to the lighting instruments.
In modern Lighting systems, patching is controlled by the lighting console. In older systems power may pass through a hard patch panel to be assigned to a circuit.
Dimmers come in a variety of formats from portable dimmer packs (aka. Shoebox dimmers) to Rack mount assemblies. In the Portable Dimmers, DMX addressing is controlled per pack, whereas the Rack mounted dimmers are addressed through a control module.
Dimmers should be cleaned regularly to keep them free of dust.
Links to extra articles about dimmers:
Dimmer feeds--How much power is enough?
Dimmer response time
Dimmer rise time
Dimmer rise time, IGBT
Links to common (and not-so-common) dimmer types:
Dimmer, Forward Phase-Control
Dimmer, Phase Control
Dimmer, Reverse Phase-Control
Dimmer, Sine Wave