In the context of numerical linear algebra, what does the 'condition number' of a matrix measure?

Sensitivity of the output to small changes in input

The condition number $\kappa(A) = \|A\| \cdot \|A^{-1}\|$ quantifies how much the solution $x$ of $Ax=b$ changes relative to small changes in $b$. A high condition number indicates an 'ill-conditioned' matrix where results are prone to numerical error.