Think of salt as a 'battery booster' for rust; just as a battery makes a circuit work faster, salt makes the electrochemical 'circuit' of rusting run much more efficiently.

The corrosion of iron is a redox reaction. In the presence of moisture and oxygen, iron ($Fe$) acts as the anode, losing electrons ($Fe \rightarrow Fe^{2+} + 2e^-$). The presence of salt ions ($Na^+$ and $Cl^-$) increases the electrical conductivity of the electrolyte layer on the metal surface, facilitating the flow of electrons and thus accelerating the cathodic reduction of oxygen, which forms rust ($Fe_2O_3 \cdot xH_2O$).

Always remember that corrosion is an electrochemical process; any substance that increases the conductivity of the medium surrounding the metal will accelerate the rate of degradation.