The burners in a furnace permit the flow of gas, which is ignited by the pilot that sits beneath the burners. The outside of the heat exchanger is heated by the burners and transfers its warmth to breathable air, which first flows by the heat exchanger in a nearby, but separate, component before venting to the rest of the house. The burning gas produces toxic fumes that are vented to the outdoors from inside the heat exchanger.
The most common reason for a pilot to be blown out by a cracked heat exchanger is due to the furnace fan. Many thermostats allow the fan to operate separately from the heating component of the unit. If the fan is on and there is no call for heat, the blowing air can potentially be forced through the heat exchanger to the pilot if the crack is big enough and in the right location.
A gust of air coming down the chimney can blow out the pilot. If the chimney is not in the correct location or is not the proper height, air can potentially flow down to blow out the pilot when there is a cracked heat exchanger. It is also possible for a worn-out chimney liner to allow air down to the pilot.