When I trip the circuit breaker for my electric stove, the lights and timer still have power. How is that possible?

Assuming you have a 2 pole circuit breaker for the stove your shutting off, could be a separate 120 volt circuit for the lights and timer.

Or you could have a breaker that does not open the circuit.

If you have a multimeter, go to the breaker in question and test both legs of the breaker to see if one leg stays hot with the breaker handle in the off position.