Gentrification, as a term, has long ago left the sociological literature and entered the common speech, usually in a pejorative way. The problem with this is, while the term might have meant something fairly specific in the original research (although I doubt it was very specific), it has come to mean a number of things in its common usage.
When using sociological terms, it is important to operationalize them. Gentrification is the process of a more affluent population moving into an area inhabited by a less affluent population. While this sounds like a good definition, defining it further is somewhat problematic. On the issue of "affluence", there is many ways to operationalize that. Furthermore, how is the difference between them defined? Every neighborhood or demographic area has a range of possible incomes, so how far above the range of incomes do newcomers have to be before they are gentrifiers? And as for "moving in", we have the same question: since there will almost always be some residents of an area with an income well above the mean, how much of an influx has to happen before the area is "gentrified"? 10%? 20%? 50%? Thus, very different definitions of what gentrification means could be given. It could be 10% of the people moving into an area have an income of 20% over the old average, or it could be 50% of the people moving into an area have an income of 50% over the old average.
This is not a theoretical question, although the plain numbers may make it sound like one. I will take two different examples of something that could be called "gentrification", and explain why they look very different on the ground. These are two stories from my hometown of Portland, Oregon.
The Pearl District was, in the early 1990s, a large section bordering downtown Portland that had previously been a light industrial district, but now consisted of mostly abandoned or semi-abandoned buildings, as well as some low-income housing. It also smelled like a brewery. Due to a deliberate effort by the Portland Development Commission and some developers, the area was torn down, rebuilt, and filled with condominiums and trendy restaurants and galleries. Walking through the Pearl, it is hard to imagine any way to exaggerate what it is like. It is a good place to get a cupcake for five dollars, or get aromatherapy for your dog. The residents of the Pearl are largely of the so-called creative class, and are paying top-dollar for their condominiums. It would be hard not to call the Pearl "gentrification".
Across the river is the large, amorphous district that makes up North and part of Northeast Portland: An area of at least a dozen square miles, taking in different residential, commercial and industrial districts. This area is also, traditionally, the center of Portland's African-American community. In the 1980s, it had a mostly exaggerated reputation of a "dangerous" area. However, it was a large area, and while parts of it were very poor, much of it was working class or lower-middle class. What has happened, slowly, in the past ten years or so is that the area has lost some of its stigma, and many lower-middle class or middle-class people have moved in. Many of these people are young, white, and well-educated, but not quite the type of people who can pay a quarter-million dollar for a 1500 sq. ft. condo. In fact, in November of 2004, I was one of these people. I had just left school, and got kicked out of college housing, and needed a place to live very, very quickly. Craigslist advised me of a room for rent in North Portland for a reasonable price, so I moved there as quickly as I could. So I, as a young desperate person, suddenly became one of the gentry.
Hopefully these stories, which while somewhat detailed are still not detailed enough to give the actual feeling of how these neighborhoods have changed, can give a bit of a hint of the problem with "gentrification". In the first example, a decision was made by a small group of people, including government agencies and developers, to take a small group of ground, and drastically change its characters and sell it to some very wealthy people. In the second, over a much larger amount of time, an area slowly changed its character, as people moved into it out of necessity. Yet both of these are "gentrification". This is why I think the term "gentrification" is poorly characterized, and not very good as a serious sociological term.