High-number: Before 1974, Topps issued their annual sets in series of fifty to two-hundred cards each, ordered numerically. From two to six series constituted a set. The last series or two are called the "high-numbers" simply because they were the at the high end of the set numbering.
This is significant because the later series were ordered more and more lightly as the year wore on. Back then, baseball cards first appeared in late March or early April, with new series appearing every six weeks or so until October. Making an assumption, I suspect that kids back then had just as short an attention span as they do now, coupled with the distractions of returning to school and shorter days, and the other events of the fall. Later series weren't ordered as heavily as the first few. Plus there are stories of distribution problems; some series simply didn't make it to some parts of the country.
Jumping ahead to the modern card market, we find that scarcity is the driving force in the economics of the market, and the initially scarce high-numbered cards of yesteryear are some top dollar items. 1952 Topps high-numbers go for a couple hundred each, even for the lamest of bench warmers, because there just aren't many out there and it is one of the great sets of all time.
Since the return of multiple series, though, this terminology hasn't returned. Almost every multiple series set is just two series, so using the terms high and low-numbers is a little silly. From 1989 until 1992 Upper Deck sets use the term for their late-season update releases. Pinnacle Brands tried reviving the high-number concept with their 1997 Select baseball set, but like most Pinnacle sets of the era, it was ignored by The Hobby.
With the recent trends towards SP cards, which tend to be placed at the end of a set, "high-numbers" is acquiring an additional meaning. Though not widespread, if someone offers to sell you some 1999 Ultra high-numbers, he just means the short-printed cards at the end of the set, not some unknown third series.