Time Invariance
A system is called "Time Invariant" if its output does not depend directly on time. A time shifted function is a good example of a time invariant. Though it might be shifted slightly or greatly by time, the output of the function itself is not directly effected by time. Take the following example, for instance.
Function: $ x(t) = 2cos(t-T) $
This function can be shifted by a time T but eventually the output of the function will be the same. Now consider if the same function is multiplied by a factor of (t-T).
Function: $ x(t) = 2(t-T)cos(t-T) $
This function is most definitely dependent on time. As time increases, so does the magnitude of the output of the function x(t).
