Let us come from basics.
We call flow of charge is called current. And in order to create the flow, we need a force. That we are achieving the positive charge and negative charge.
As positive charge and negative charge attract each other we create a circuit and makes it flow.
Consider the diagram:
Here in order to glow the bulb, we need current (flow of charge) So we connecting a source, here battery.
Once we make the circuit complete +ve charge and -ve charge attracts each other. Thus creating a flow of electrons i.e. current. This complete circuit is called closed circuit.
If you disconnect any side of the source or anywhere along the line the +ve charge and – charge cannot have any kind of attraction between each other resulting from an absence of flow of electrons. This incomplete circuit is called open circuit.
Difference: Closed circuit conducts electricity, whereas Open circuit does not conduct electricity.