This is what the Beckett oil burner looks like when you flip the transformer open, the 2 springs put out 10,000 volts, the two white ceramic things are the electrodes the springs from the transformer send 10,000 volts to the tips of the electrodes that are positioned in front of the oil nozzle, causing the oil to ignite.
The silver thing to the left with 2 oil lines connected to it is an oil delay switch it stops the oil from being pumped for a few seconds and stops the oil from dripping when the burner turns off.