Wikipedia states that the term "The Long Tail", as a proper noun, was first coined by Chris Anderson. The term was inspired by an essay titled, "Power Laws, Weblogs, and Inequality". In the essay Clay Shirky shows the distribution of inbound links for 433 blogs. The top two blogs had 5% of all inbound links, while the other 431 blogs shared the other 95%. The 95% is The Long Tail.
The Long Tail, as a business model, is about going wide with your product line. The idea being that the sales from the few best sellers will be eclipsed by the rest. Amazon is a good example of The Long Tail, where a vast majority of their sales come from products that don't sell well. Therefore, the Web 2.0 model is to offer a wider selection in your space, and not a focused one.
The trick of course is to make this model profitable. Adding products to your offerings can be cost prohibitive. For example, on longtail.com there is a post about The Long Tail as applied to the publishing industry. The problem for publishers is that printing a short run is more costly per book than a long run, but printing a long run on a book that doesn't sell fills expensive storage space. So popular books are cheaper to produce than unpopular ones, which is why books go out of print, it is just too costly to produce for the small demand. So the challenge is to find a way to equalize the publishing cost, no matter what the run size. If you can do that, then you will sell more unpopular books than you do popular ones.
Another example of The Long Tail is the iTunes service, where you can buy music for download. There is little additional expense between iTunes carrying an inventory of 100 songs, or 1 million songs. This makes it possible to sell not only the big hits, but a million other songs that might only sell a few copies a year. In the end, those million songs combined will sell more units than the top hits. This is what The Long Tail is all about.
One last thing I want to mention is The Long Tail Camp, an ongoing event for the next 10 years or so (the event has a long tail). This site encourages, and to a point facilitates, the gathering of groups for discussions on The Long Tail, and how it can be applied to particular industries.