A
short circuit is nothing more than a stretch of wire in a circuit. There is no potential difference, or
voltage, across a short circuit, and the same amount of current runs throughout it. Short circuits are nothing special. However, it is useful to use short circuits (and their counterparts, open circuits) as
abstractions.
Consider a simple switch. When it's on, current flows through and it acts like a short circuit. When it's off, it acts like an open circuit. If you put a switch in parallel with a resistor, you can make it so either all or none of the current will flow through the resistor. This type of abstraction can carry over to other elements, like capacitors, inductors, even transistors and diodes.
Capacitors build up charge, while inductors resist changes in current. A capacitor with no charge built up on it will have no voltage across it, and thus it acts as a short circuit. When an inductor is fully charged, it does not attempt to slow the change in current any longer. It acts as a short circuit, letting all the current go by. This allows you to analyze these elements' behavior exactly at certain times. This knowledge is very handy for use in zero-input and zero-state response.
A switch is a very poor model for a transistor, especially a MOSFET. Usually, a resistor or a dependent current source will be used to model a MOSFET. On the other hand, an ideal diode behaves exactly like a voltage dependent switch. Ideal diodes behave like short circuits whenever the voltage across them is positive. They shut off whenever the voltage across them is negative. Real diodes actually turn on when the voltage across them is about + 0.6 volts.
If you start ripping random wires out of a circuit, someone may be concerned about you short-circuiting it. This is completely wrong, and is a common misconception among people who don't know much about circuits. If you do this, you're not short-circuiting it, you're causing open circuits. The end result will usually be the same; the circuit will no longer work. Since the effect of causing open circuits and short circuits is the same, people assume that they are the same thing.