Shotgun barrel back-boring is nothing more than the machining process of reaming or boring a shotgun barrel to a larger interior diameter. This is usually done by a very knowledgeable gunsmith in the efforts to save a rusted shotgun barrel and usually is done as a few thousandths of an inch clean up pass through the barrel. The barrel is then usually polished and burnished inside, restoring the barrels interior back to a useable state of condition do to boring.
A back-bored shotgun barrel simply means that the bore has been altered to a larger inside diameter. Back-boring of any imparticular gauge, does; beyond any doubt, add to more wider center mass and will help reduce the length of shot strings in shotguns and when done within reason it does not decrease the velocity of the shotshell load. The reason that it does not decrease the velocity is, todays plastic wads will expand a great deal to seal the bore of the shotgun and not allow gas to escape around the wad. No gas leak, no velocity lost.
As you open up the bore of a shotgun it takes less choke constriction to still get the same pattern as one with a standard bore. This is a big bonus to all that love to shoot trap and other sporting clay games because this puts more pellets into the center mass of the shot-string and over-all shortens the shot string reducing the time frame from first pellet strike to the last. Choke constriction is measured in thousands of an inch plus or minus from the bore diameter to a designated choke size such as 12 gauge bore .729 full choke= .035" constriction, modified choke - .019" constriction or improved cylinder choke = .009" constriction. Open up the bore then you open up the choke for the same choke result on a fixed choke shotgun.
If you do decide to do this. Make sure you send your barrel to someone that is experienced with this procedure and their level of finish work is excellent. This is by no means an easy process to get right. See diagram below for other issues to consider.