The simple answer is that it means different things to different people, but I will elaborate.
If you are a Amazon.com customer and you are browsing the “Product Details” of a specific book, you could interpret the Amazon.com sales-rank to be a measure of the popularity of that book. The lower the Amazon.com sales rank number, the more popular the book as determined by the number of recent sales of that title through the Amazon.com marketplace. This is true in general, but if you really want to know about the popularity of a specific title, you also need to consider the publication date and how long it has been marketed on Amazon.com. For example, a book with an Amazon.com sales-rank of 100,000 that has only been released and marketed on Amazon.com for a few days may be very popular in the near future and reach the top ten. That it is only ranked 100,000 right now is a little deceptive because the timeframe over which this rank was determined is not really long enough to measure the true popularity.
To a bookseller, the Amazon.com sales-rank is quite often correlated to how quickly a particular title might sell. A book with a very low number Amazon.com rank might be expected to sell within minutes or hours of listing, and a book with a sales rank of 4,000,000 might take several years to sell. The analogy is frequently used by booksellers when they are scouting for books to add to their inventory. If a bookseller finds a book that has an online value of $10, an Amazon.com sales rank of 2,105,878, and he/she is faced with buying it for $4, they are apt to pass, but if the sales rank were 45,017, it might suddenly be a book worth adding to their inventory.
In scouting for books, I do look at the Amazon.com sales rank for higher priced books because I do not want to stack a lot of firewood on my shelves, but it is certainly not the measure I use for most book purchases. The scientist in me wanted to know more, so I compiled the Amazon.com rank data for thousands of the books I have sold, using Amazon.com rank at both at the time I purchased them and at the time I sold them respectively. Being an engineer, I had to collect and torture the data to see if there was any correlation between the Amazon.com sales rank and the time it takes to sell a book. Indeed there is, at least in my experience, and doing a curve fit to the data yielded a correlation coefficient of 0.93. The wellness of fit of the data is particularly apparent in a semi-logarithmic plot.
So, you see, there is a meaning to the Amazon.com sales rank.
For the book buyer it is a measure of a book’s popularity.
For the bookseller, it is a measure of how quickly a book might sell and or whether or not the book might just be firewood.
For the engineer, it is just a bunch more data that can be tortured into a confession of sorts.