Well, having asked the question I then went to Bing.com to investigate further. I was surprised to find the answer quickly. I found it here:
and I reproduce it in this way:
In the row of numbers, the smallest number shown tells you which printing of the book you have. For example, if you see "10 9 8 7 6 5 4" then you have a fourth printing.
The reason for all this is as follows: It has to do with how books were historically manufactured. Each page of a book is converted to a metal plate which is used to make impressions. If another printing run is necessary, you load the plates back onto the printing machine and off you go. But how do you indicate that this is a second printing? It would be expensive to burn a brand new plate just to change the word "first" to "second" on the copyright page. Instead, you pre-load all the printing numbers onto your master, and each time you start a new printing run, you scratch off the lowest number.
Even though a lot of book printing nowadays is done with computers rather than metal plates, the old method of indicating a printing is retained out of tradition.
Often the numbers are odd on one side, even on the other, with 10 in the middle, so that you alternately scrape off the LHS and RHS of the list of numbers. This would help to keep centered text centered on the page.