"Linear" means "Linear System" as in T(a+b)=T(a)+T(b). In practical terms this means sine wave in, sine wave out. If your system behaves as such then you have a much simpler time than if your sine wave gets distorted on the output because then that means you can no longer live in the world of Laplace transforms for understanding the PDE nature of your system. Op amps were hailed as a revelation because they behave much more ideally Linear than say a Common Emitter Amplifier, even when being constructed from non-linear components.