Definition
Time invariance system is if the input has certain time delay , T0, then the output should yield the same time delay T0.
Example
Time Invariance
System: y(t)=x(t)
x(t)->TD by t0 ->y(t)=x(t-t0)->System->z(t)=y(t)=x(t-t0)
x(t)->System->y(t)=x(t)->TD by t0->z(t)=y(t-t0)=x(t-t0)
The output are equal. Therefore it's time invariant.
Non Time Invariance
System: y(t)=t*x(t)
x(t)->TD by t0 ->y(t)=t*x(t-t0)->System->z(t)=t*y(t)=t*x(t-t0)
x(t)->System->y(t)=t*x(t)->TD by t0->z(t)=y(t-t0)=(t-t0)*x(t-t0)
The output are not equal. Therefore it's non time invariant
