An electric circuit is a path in which electrons from a voltage or current source flow. Electric current flow in a closed path is called an electric circuit. The point where those electrons enter an electrical circuit is called the "source" of electrons.
A circuit is considered to be closed when electricity flows from an energy source to the desired endpoint of the circuit. 

A complete circuit which is not performing any actual work can still be a closed circuit. For example, a circuit connected to a dead battery may not perform any work, but it is still a closed circuit. 

Any circuit which is not complete is considered an open circuit. 
Electricity does not flow from an active energy source to the desired endpoint of the circuit since the path is not closed one; or since the path is open. 

Circuits which are manually disconnected switched off and circuits which have blown fuses, faulty wiring or missing components are all considered open circuits.