A Post-common Envelope Binary 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 Main Sequence Stars. In addition, for this type, their atypical history is explained as including a Common Envelope (CE) phase, a stage in which mass falling from one star to the other expands into a gas cloud surrounding 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.
Common envelope binary events are deduced to have occurred to explain the unexpected evolutionary stages of the two stars. Binary stars are thought to have formed as pairs, i.e., simultaneously. The characteristics of sufficiently-independent stars should reflect this identical age along with their mass, as per the Vogt-Russell Theorem. The occurrence of mass transfer between binaries was deduced to explain Algol, a star system showing such an unusual pairing 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 case, a post-common envelope binary is the result.