A Proton-coupled electron transfer (PCET) is a chemical reaction that  involves the transfer of electrons and protons from one atom to another.  The term was originally coined for single proton, single electron processes that are concerted, but the definition has relaxed to include many related processes.  Reactions that involve the concerted shift of a single electron and a single proton are often called Concerted Proton-Electron Transfer or CPET.
In PCET, the proton and the electron (i) start from different orbitals and (ii) are transferred to different atomic orbitals.  They transfer in a concerted elementary step.  CPET contrast to step-wise mechanisms in which the electron and proton are transferred sequentially.
:ET
:[HX] + [M] → [HX] + [M]
:PT
:[HX] + [M] → [X] + [HM]
:CPET
:[HX] + [M] → [X] + [HM]