Circuit

1. 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 particular type of circuit described 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 its own designated circuit line, thus dimmer numbers and circuit numbers are identical. In non-dimmer per circuit systems, there is a patch panel which assigns circuits to dimmers.
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.

2. The complete path that electricity follows, from source through switches and load [often incandescent lamp(s)] and other devices back to source.

3. During the early 1900s days of vaudeville, acts were pre-booked to tour among all of one owner's theatres in various cities. In Gypsy, Mama Rose's goal is to get her girls' act onto the Orpheum Circuit, the largest and most prestigious at the time.