One example of time invariance is playing a song. It is the same signal whether you play it at 10:01 AM or 10:06 AM. This is because the signal is the same if you listen to the song now or later. This is a 5 minute time shift that does not affect what the user observes.
An example of time variance is turning on your T.V. to a channel. If you turn it on at 10:01 AM, the first thing you see will be something different than if you turned on your T.V. at 10:06 AM. This is a 5 minute time shift which affects the signal that the observer sees.
