The most frequent cause of the problem that you are describing is the Limit Switch.
The purpose of the Sail Switch is to prevent the burner from igniting if there is not sufficient air flow, or to shut the burner off if the airflow drops below the required CFM. Your burner is igniting.
The Limit Switch is just that. The device that limits the temperature of the chamber to a safe level. If the Limit Switch is not returning to the normal (open on some furnaces, closed on others) state, the furnace will not cycle back on until shut completely off and turned back on.