Definition
A system is called 'time invariant' if for any input signal x(t) and for any time to that is a real number, the response to the shifted input x(t-To) is the shifted output y(t-To).
This is saying that for order for a signal to be considered 'time invariant' i must be able to put any signal through the system that has gone through a time shift, and i should get out another signal with the same time shift.
Another way to look at time invariance is that if I had a signal x(t) and i put i through a time delay of To, then through the system, I should get the same output if i put x(t) through the system first, and then shifted the output function of the system by To.
Example of Time Invariant System
x(t) \to
