A post-common envelope binary (PCEB) is one type of binary star showing an unusual history, i.e., a pair that doesn't appear to fit the typical history associated with independent main sequence stars. Their particular atypical history is presumed to include a common envelope (CE) phase, a phase during which mass falling from one star to the other expands into a gas cloud that surrounds them both, i.e., an envelope common to both stars. A star in that phase is called a common envelope binary (CEB) and the phase is called a common envelope binary event (CEBE), the word event used because the phase is assumed to be very short.
Past common envelope binary events are deduced to explain the unexpected evolutionary stages of the two stars. Binary stars are thought to generally form in pairs (simultaneously) and the characteristics of sufficiently-independent stars should reflect this identical age along with their mass, as per the Vogt-Russell theorem. An occurrence of mass transfer between binaries explains Algol, a star system with such a mismatched pair of stars. I don't think Algol is considered a post-common envelope binary, but models explaining some other binary systems incorporate a common envelope phase in their history. Such a common envelope phase might end with the two stars coalescing, or with the envelope blown away, or leaking away. In the latter cases, a post-common envelope binary is the result.