from the wiktionary, my favorite online dictionary:
4. (beekeeping, archaic) An empty box added beneath a full one in a beehive to give the colony more room to expand or store honey.
compare to supering:
1. (beekeeping) To add or to place a super atop the existing boxes of the beehive.
supering is more common, at least in North America. one big advantage of nadiring, though, is that the bees can continually build downward as boxes are harvested from the top and returned to the bottom empty. in this way, comb is generally renewed every two to four years. that could be particularly important in regions with persistent pollutants (read: everywhere) that would otherwise build up in the comb and possibly lead to trouble for the bees.
I personally believe that supering can lead to higher honey yields, but at the expense of the colony's health. in circumstances that are rare in my region, supering is the only simple way to prevent honeybinding, so it does make sense in some cases.