The meaning of the phrase 'Once in a Blue Moon' is something that happens very rarely. However, in the past, the meaning of the phrase was something that was preposterous and unreasonable.
Example of use: "I have only 2 more months till my wedding, so I allow myself to eat fast food only once in a blue moon."
The term 'Blue moon' describes an event when four full moons appear in a particular season (normally they are only three for each season), the third moon is called a Blue moon. The first recorded use of the phrase, in its modern meaning, was in an 1821 book by Pierce Egan 'Real Life in London': "… How's Barry and Ben? – haven't seen you this blue moon."