Merriam-Webster has a short, snappy definition that says simply "Indistinguishable from other places in appearance or character". If you go to college-level geography, entire dissertations are written about the subject. I like the Merriam-Webster version because it's open ended enough to cover a lot of bases but conveys the concept well.
Essentially, placelessness is the loss of a unique sense of place and increasing uniformity. For instance, your old home town's unique, defining features, such as an older main street with a local barber shop (The Leather Strop), a Tavern (Joe and Elaine's) and an independent hardware store (Precortt's) may have all been replaced (or at least are getting pushed on), by Great Clips, Applebee's and a Lowe's, respectively. Another example would be the destruction of many small downtowns in rural Minnesota by the installation of a Wal*Mart.
We saw a number of things in Florida that got me to thinking about not only placelessness, but also the broader direction of our culture and what the drivers of culture are. I saw at least one and sometimes two or more McDonald's in every town we drove through in Florida. I saw probably half a dozen Bed, Bath & Beyond stores in Jacksonville and St. Augustine alone.
The concept of placelessness goes beyond urban planning and geography, however. In The Tipping Point, Malcom Gladwell tries to explain how little things can become big things ("go viral"). He starts with a story about how Hush Puppy shoes got really popular because they found a niche or were adopted by a sector of the population (hipsters grabbed onto Hush Puppies, if I recall the book correctly). Gladwell has a social science perspective that helps explain the non-geographic placelessness phenomena.
I have been noticing other non-geographic trends that also seem to lend themselves to placelessness - examples might include top 40 radio, Brittany Spears and Hannah Montana, NASCAR, "Who Wants to be a Millionaire" and "American Idol", Crocs, ClearChannel Broadcasting, McDonald's, REI and Trek/Giant/Specialized. These all fall into the "placeless" category for me. These are all products or phenomena that are pushing out smaller, more diverse competitors by providing a product, or products, that may not be better, but have very broad market appeal and/or superior marketing resources.
I think in many respects, these are the lowest common denominator; it's not that the products are inferior, but rather they appeal to the largest population of potential customers. I might almost categorize these as "the least offensive". One of my criticisms of Consumer Reports is that they seem to pander to this mindset - they seem to strive to find the most generic or universally acceptable product with the broadest appeal to consumers rather than delving into which product is right for an individual consumer - read a bicycle review from them and you will see what I mean.
I much prefer the diversity and uniqueness of local, independent retailers and restaurants when I can find them. Hopefully, we will not lose too many more of these in the tough economy, but I fear that economics and sociology of sales will be a threat to this type of diversity for the foreseeable future.