Overboring started with the clay gamers,tho Nash Buckingham was doing some research on long range waterfowling in the 40s and 50s and used a Fox double with lengthened forcing cones and nigh 11 ga bbls.
The premise is that with less shot hitting the bore, there's less distortion and the shot fly true, staying in the pattern. Oft those pellets we see on the edge on the pattern are leaving it. Over boring(sometimes called back boring) and longer forcing cones both aid this.
Many smiths refuse to overbore bbls, removing bbl steel isn't a step in the right direction.
Downside, slug groups usually bite from overbored bbls, I understand.
FYI, my chokeless HD 870 patterns 00 into 3-5" at 10 yards, for comparison. No overbore, but a cone job.