An open circuit means that the circuit is not complete. It is broken somewhere. It can be a gap remaining in the connection. 

Suppose you connect two copper wires to a small bulb and connect the other end of one wire with a battery. You still have to connect the other end of the second wire to the battery to make the bulb glow. When this type of gap remains in a circuit, the circuit is called an open circuit.

As the connection is not complete, potential difference is not created between the two ends of bulb. So, electrons do not move in a specific direction and so the current does not flow.

A circuit must be complete for the switch to be "on" if there is any break or open spot, it is an "open circuit".

Open circuit are not complete. therefore, electricity doesn't flow.