Definition: Time-Invariant System
A system is said to be "time-invariant" if time shifting any input x(t) (or x[n]) yields the same result as time shifting the response to x(t) (or x[n]) by the same magnitude.
Definition: Time-Variant System
A system is said to be "time-variant" if time shifting any input x(t) (or x[n]) does NOT yield the same result as time shifting the response to x(t) (or x[n]) by the same magnitude.