Thanks! I think I'm starting to understand it now. When the switch is flicked, the field starts doing its thing, whatever that is, and thus electricity begins to flow "in the vicinity" of the lightbulb and the switch. That's why the lightbulb turns on.

Having said that, if there was another lightbulb connected at the opposite extreme of the circuit, say, half a lightyear away, then that lightbulb wouldn't immediately turn on. It will turn on eventually, but like, six months later. Would that be correct?