An engine backfiring upon accelerating is usually caused by the ignition of the air and fuel mixture while it is still in the intake manifold.
The backfiring due to the ignition of the air and fuel mixture is usually caused by the inlet valve sticking or leaking or because there is an ignition system fault.
You could have a bad fuel filter causing low fuel pressure or you could have bad spark plugs, bad ignition coils, bad ignition coil, bad fuel injectors etc.
Or the timing could be off due to a timing belt being stretched.
Other causes of a car backfiring when accelerating are bad oxygen sensors, bad catalytic converter or even a weak fuel pump.
If your car continues to backfire I would advise you to take it to mechanic to look at it because it could eventually lead to engine damage eventually.
Also when your cars fuel and air mixture are not right then your fuel usage goes up so you would get less miles per gallon from your vehicle.