When something occurs once in a blue moon, it almost never happens. If you very rarely sleep through your alarm, you only oversleep once in a blue moon.
The idiom once in a blue moon is a more colorful way to say "rarely" or "hardly ever." If you don't have much of a sweet tooth, you probably only eat dessert once in a blue moon. This expression is often associated with the astronomical "blue moon," which is most commonly defined today as the second full moon in a calendar month — a rare phenomenon that only happens about once every two or three years.