A backfire occurs when the mixture's ignition is synchronized to the valve opening and closing.

Usually it's a matter of a (premature) ignition happening when the intake valve is still open -- after all, if both valves are closed the explosion isn't going anywhere (it's confined to the combustion chamber).
Possibilities include an intake valve that became stuck and stayed open when the spark fired the mixture.
Or it could be some hot piece of metal in the cylinder, or somehow the spark fired very early, prematurely igniting the mixture before the intake valve closed.