There are a bunch of different gasoline engine ignition systems, and all of them are pretty strange. Mine is a flywheel magneto, which is extremely clever, cheap, and reliable, but not nearly as simple in theory as some others.
You must begin with understanding how a simple coil of wire and, say, a flashlight cell can produce several thousand volts: enough to give the young experimenter (me) a memorable jolt when the wires are held in the hand and the battery is disconnected from the coil. Every ignition system depends upon this basic principle, for there's really no other way to produce the necessary 12,000 volts for a spark plug.
The ignition points are just a switch whose contacts are exceptionally durable. The coil consists of insulated wire that's wound around an iron bar hundreds of times. We can wind several coils around the same bar. The condenser, or capacitor, consists of two pieces of aluminum foil separated by a piece of plastic wrap, all folded up so it fits in that little round metal case. And there are magnets. That's it.
The magic is in the physics, which tells us that if the amount of magnetism in a coil *changes*, a voltage (electrical pressure) will be produced across the ends of that coil's wire. And: the strength of that voltage depends upon how fast we change the amount of magnetism through our coil.