If there is a gap or break in the circuit, the electricity will not flow through it. This is called an incomplete or open circuit.
An incomplete circuit is an open circuit; i.e. some part of the circuit isn't connected to anything.
Or think of it like this: A circuit is complete when there exists a complete (or closed loop) path for the electrons to flow through it. Also known as a closed circuit. If this is not the case, then it is an incomplete (or open) circuit.