Generic "working" of a simple oil boiler (conventional flue without run on timer) -
Power applied to burner via external controls and boiler thermostat (also any boiler overheat thermostat with normally closed contacts).
Most sequence control boxes check no flame present before one should be there, Burner motor starts and in some units ignition arc starts simultaneously others after short delay. The fan runs to purge the combustion chamber. The oil pump runs with the motor but no oil delivered until the purge delay expires when the oil solenoid is energised open and oil is sprayed into the chamber past the ignition arc which lights the oil flame. The light of the flame is detected, the arc turned off and the flame continues to burn until the heat demand is satisfied when the thermostatic controls remove power from the burner.
If a too early light is detected the sequence control goes to "false light lockout" If a proper flame is not detected shortly after the oil solenoid opens the sequence control goes to lockout. In lockout the burner stops, an alarm light illuminates and resetting requires manual reset.
Occasional failure to ignite can happen but if more than once in a blue moon further investigation is required.