surface of last scattering

The surface of last scattering (aka last scattering surface) is the spherical shell-shaped region around us from which the photons of the cosmic microwave background (CMB) are arriving, i.e., given the photons' speed, it is the shell-shaped region of space at the distance that they necessarily came from. What we "see" as we observe the CMB is the surface of last scattering. It is the most distant thing we see, everything else we observe being in front of it.

Before recombination, the photons were constantly scattered within the dense plasma of the time (something like light within fog). Pretty much by definition, recombination indicates the time when photons began moving freely (free streaming) and any photons that happened to be headed our way and were just at the distance to reach us right now constitute what we are observing. The photons moving toward us that happened to begin their free streaming at a point closer to us have already reached us and photons that began their free streaming further from us have yet to reach us. When the latter arrive, their origin is where the surface of last scattering will be. Thus it constantly moves away from us as the passage of time increases the time it took for the photons to reach us, but the Hubble expansion is also carrying that point away from us. However, in our lifetime, the increase is not overly significant compared to the universe as a whole.