I have a 92 Honda Civic DX. I took it to Honda recently because it sounds like it's backfiring. They told me that it in fact was not backfiring, but it has an aftermarket muffler and that this was the culprit. An exhaust leak in the tubing, and broken baffling was causing this noise apparently. To me it makes me so nervous because it sounds so much like a backfire. I was just looking for an explanation as to why when an exhaust system deteriorates it makes this noise? An explanation would really help to ease my mind. Thanks.

What they told you sounds like one possible reason. The muffler could be getting too much fuel.
Or you might need a tune up, it could be the ignition coil, or the carborator, or something with the distributor, any of that should be something they would check when doing a tune up.

I just had timing and coil problems. In the midst of fixing that I replaced the ICM, Coil, Spark Plugs, Plug wires, filters, engine retimed, They rechecked the timing when I went in this last time and it was fine. What else could cause this?

Oh and it's not carberated its fuel injected.

Also the aftermarket exhaust is a cheapy... I put it on when I was 16 and just never replaced it to stock. Now that it's been on there 5 years it's getting really irritating... I just want to make sure it's not anything that's going to leave me sit on the side of the road.

Yeah I would say you need to replace the exhaust and see what happens then.