what is a potential difference

Simply put, potential difference is the difference in energy of two location. So if you are standing at a pole 3m high and I'm at a pole 10m high, we have a potential difference of 10 - 3= 7m.
 
The same concept applies to electrical and electronics, which your query is. The same concept for fluid/hydrostatics is called as head difference.
 
Now coming to your question, technically.
 
The flow of electricity is attributed entirely to the potential difference. As mentioned above, its basically the difference in energy at two locations. Consider a piece of wire, unconnected. Since both the ends of the cable are at same energy level, there won't be any potential difference, hence no flow of current.
 
You can imagine this as little water spilled on your dining table. The water will not flow until your table is leveled. Now if you will tilt the table to any side, leading to a difference in level over the table, the water will start to flow from the higher level to the lower one. Same as in a case of a rolling ball (high to low).
 
Coming back to your piece of wire. If you decrease or increase the level at one end, say by attaching a battery and complete the circuit, there shall be a potential difference, and the current shall start to flow.
 
Technically, potential difference can be defined as the amount of energy required to move a charge around a circuit. It is measured in Volts and commonly called as 'Voltage'.
So next time you read your batteries rating as 1.5V or 6V or 12V, that would be no different than the potential difference between its two terminals (+ &) -.
 
The potential difference shall exist for any difference in energy. So there shall be a potential difference between two terminals at 12V and neutral respectively. It shall exist for terminals at 12V and 8V too. And for -5V and -10V as well.
 
Potential difference is almost similar to emf or electro motive force, difference being that emf is for the open circuits.

The amount of energy per unit charge needed to move a charged particle from a reference point to a designated point in a static electric field; voltage. Also called potential.

the difference in electric potential between two points is called potential difference.