Engine damage can eventually occur if the engine backfire gets worse or is caused by something worse inside the engine.
A backfire on an engine can be caused by several different things such as bad ignition timing, the engine ignition timing not being set correctly or bad spark plugs or a bad distributor or distributor cap and rotor.
An intake gasket leak can also cause the engine to run lean which can also lead to an engine backfiring and it's best to get the engine backfiring fixed as soon as possible because it does mean that something is wrong and your fuel mileage is likely decreasing as well.
I would get the engine checked out to find out what exactly is causing the engine backfire and get it fixed before it causes major problems and more costly problems.