Step 1: Understanding specific conductance.
Specific conductance (or conductivity, $\kappa$) is the conductance of 1 cm$^3$ of solution placed between two electrodes of 1 cm$^2$ area separated by 1 cm.
Step 2: Relation of conductance and resistance.
Conductance = $\dfrac{1}{\text{Resistance}}$ = ohm$^{-1}$.
Since specific conductance accounts for distance (cm) and area (cm$^2$), its unit becomes:
\[
\text{Unit of specific conductance} = \text{ohm}^{-1} \ \text{cm}^{-1}.
\]
Step 3: Conclusion.
Thus, the unit of specific conductance is cm$^{-1}$ ohm$^{-1}$.
Final Answer:
\[
\boxed{\text{cm}^{-1} \ \text{ohm}^{-1}}
\]