Formally, a circuit is a path from a high voltage source, on a battery, generator, power supply, etc to other elements in the circuit (e.g. resistors, etc), and then back to the paired low-voltage terminal on the source.
The path must be a loop so that electrons can circulate, forming a current, otherwise they will pile up at one end, and then nothing further will happen. The path may include branches, so that some of the electrons take one branch, and some another.
More loosely, the term 'circuit' (or circuitry) is used to describe a hardware assembly.