Backfire is either deliberate or not. I have come across cars
that installed flame thrower to emulate extreme backfire. That is
cool but dangrous. Can use it for bbq at times.
Here's my share of explanation. Its not about clearing carbon or
oil!
What causes Backfiring really?
More often than not, backfire occurs when a driver downshifts and
throttle. This is caused by a lean condition. What happens is that
the air fuel mixture leans out enough to where is fails to ignite
consistently. This, in turn allows some un-burnt fuel to get into
the exhaust pipes. Then when the engine does fire, these unburnt
gases are ignited in the exhaust pipe, causing the backfire.
As for Rotary Engines, here's the link for the most detailed
explanation.
http://travel.howstuffworks.com/rotary-engine2.htm