Linearity is defined as a system that contains superposition in the book(Signals and Systems 2nd ed. Oppenheim, 53). How I see it is if the input signal has a magnitude applied to it the output should have a magnitude applied to it. Also if two signals are added it would be as if each signal had went through the system and then had been added.
Linear System Example
$ Y(t) = x(t) $
$ ax_1(t)+bx_2(t) -> [System] -> ay_1(t) + by_2(t) $
