The term makes more sense once you stop saying it wrong. It's "Overbore", not overbored. IE this cartridge case is "overbore" for this caliber.
It has to do with the case capacity to bore diameter, and how the case can hold more powder than can be used in that caliber barrel.
One thing that has changed (for many cartridges that were previously considered overbore) is the powders themselves. Where in the 50's there was no powder available that could make use of the capacity, today we have several "new" powders that can.
