An implementation is a compiler or interpreter for a programming language; This is a way to translate language instructions into behavior. The most common language with several implementations today is probably JavaScript.
When people talk about implementation, it is often in the context of the need to solve problems arising from the presence of several. There are advantages - your loved one will do what you like, but problems can be disappointing. Since Chrome and Firefox, as well as IE and Safari behave differently with the same JavaScript code, web developers have to spend a lot of time testing their code in different browsers, determining which one you are using, and adapting the code to several different sets of libraries, errors, etc.
Some languages are defined by the standard implementation (ruby, perl, python), and not by the document, so you do not hear about several implementations of these. Even in these languages, you have a related problem with different versions having different behavior.
Implementations are not a new phenomenon: in his school days, Bill Gates began writing one of many BASIC implementations, for example.
What makes problems worse with the Schema than with other languages is that the specification is intentionally small - trying to specify very little. The advantage is that people who develop programming languages can create a new experimental implementation of the circuit with neat new properties relatively quickly. Once they do, they can argue that even the small language they write is “useful,” because others have shown how to expand the small language into useful. However, there is a lot of work in this "simple programming question", and each implementation must make the most different decisions on its own, so the differences between the implementations are many and significant. Thus, the problems associated with several implementations are numerous in the Scheme compared to more specific languages.
The Scheme community recognizes this problem along with a small specification and is actively working on how to make the transition from an experimental language to a useful language more understandable with new versions of the standard. http://scheme-reports.org/
At the moment (2010), I personally recommend that new users start working in the PLT Scheme, and I am glad that you started there. Do not let many implementation problems scare you: there is great benefit for working in a language that the developers of the programming language have developed for themselves. PLT has a large community and a good set of libraries to help you overcome the difficulties described above.
Best, Grem