A circuit, simply put, is an enclosed circular path, usually of wire, that allows electrons to flow through it. Electrons are little guys that make up what we know as electricity.
There are two kinds of electrical systems, but we'll just briefly discuss the type of current that is used for a wired invisible fence.
A direct current system is when the electrons in the wire can only move in one direction. This is similar to a one-way street, where traffic can only move, well, one way.
The electrons are forced through the wire. It is the electron's movement through the wire that produces power and performs work.
In this case, the electrons broadcast a radio frequency.
That broadcast doesn't flow into the wire unless the path back out is also completed by the wire entering the transmitter unit.
If the wire is severed or disconnected, the electrons don't flow.
So you have to set up the fence wire as an open circuit, but there are tricks to make sure your dog can pass over safe areas in the invisible fence while still creating a closed-loop circuit with the wire.