Recombination is a point in the history of the universe around redshift 1090, at about 378k years after the Big Bang, when electrons and protons paired up to form neutral hydrogen atoms. In this usage, the term is a misnomer because this "recombination" is actually the first time the electrons and protons were together.
This ended the photon epoch, when photons' mean free path (between electrons and protons) was short due to Compton scattering by electrons, which had made space opaque. This lengthening of the photon mean free path is known as the photon decoupling, when one of the conditions of thermodynamic equilibrium was removed.
It was the beginning of the dark age, when the universe was transparent but there were not yet stars. The freed photons traveled freely, generally with no interaction with matter, and now constitute the cosmic microwave background.
The term recombination is also used for the pairing of ions and electrons in other circumstances, which happens in many astronomical phenomena, e.g., the interior of stars. The resulting emission is called free-bound emission.