What is a short circuit at the electron level?
The name "Short Circuit" comes from an unintentional path for the electrons which is "shorter" than that we intend.

Crudely speaking, the electrons will follow the path of least resistance.  Normally we control that flow through our circuit using the components, such as resistors, capacitors, transistors, etc.  When an unintentional route between two points is created that is of a lower resistance (thus "shorter") than we want, that is where the electrons will prefer to go.  This is what we term a "short circuit".

On an electron level it is no different to any other part of the circuit, but from our point of view it is a bad thing that causes things to happen that we didn't want.