Circuit

In the traditional electrical sense, a circuit is any complete system involving the flow of electrons from point A to point B. In the lighting world, a circuit generally refers to a particuar type of circuit discribed below.

A circuit is a numbered cable that carries power to a numbered outlet where you plug instruments in. In a Dimmer per circuit system, each dimmer has it's own designated circuit line. In non-dimmer per circuit systems there is a patch panel which sends power to any circuit you chose.
Remember, the number relationship between circuits, dimmers and Channels may or may not be fixed. Channel #4 on the light console can turn on dimmer #4 and send power to circuit #4. OR channel #4 can turn on dimmer #29 and send power to circuit #87. It all depends on how things are patched in the system.