One of the first thing you should try out is blinking 2 or more LEDs at different frequencies. This can only be accomplished with a non-blocking state machine, so the usefulness and the purpose of a millis() based timer becomes self-evident.
Six or more LEDs with periods in the range of 200-500 ms, but with small differences of 1 or 2 ms, make interesting chasing patterns if you watch them go for a few minutes.