A Quinfecta is the very rare occurrence where, upon defeat, a single enemy drops five different rewards to a single character. An inspiration, regular enhancement, Base Salvage, Invention Salvage, and a Invention Recipe. Each drop is checked on a separate random chance, so there is a very, very small, but not zero, chance of getting all five at the same time. The term is apparently an internal developer term for the event that was revealed to the player base the first time a discussion of the event occurred on the main boards.
It is theoretically possible to get a six-way drop against certain Devouring Earth enemies. DE Monsters drop Essence of the Earth special inspirations in addition to all regular drops. And there is speculation that Ambrosia from the Eden Trial may also drop in the same way.