No one seems to agree on a single definition of a courtesy flush. It can occur during or after the act of defecation, particularly when using public facilities. The idea behind it, in most cases, is to flush away any excrement that is particularly bad smelling as quickly as possible, out of courtesy to other people who might be in the restroom.
A courtesy flush is meant to be just that — a courtesy for others. If a person knows ahead of time that he is about to pay the price for last night's overindulgences, he may want to consider flushing the toilet several times during his visit in order to minimize unpleasant odors. The common belief is that most unpleasant odors are generated between delivery and reception. This type of flush is supposed to take the offending material out of the game as soon as possible, reducing the total exposure time for others.
There are others who suggest a courtesy flush should be coordinated with emanations of unknown origin. Trapped gases or explosive diarrhea can create embarrassing sounds, along with smelly odors. A well-timed flush of the toilet could cover up any unexpected developments both tangible and intangible. Arguments against a flush of this type generally involve the principles of flowing water and suction.
There is also the post-ceremonial flush. No one likes to leave a bad impression, and few things qualify as well as an unflushed or underflushed toilet. For some users, debris may be left behind, which should prompt a second flush in order to leave a clean bowl behind. Others may find multiple flushes may be in order to deal with things that don't disappear as expected.