On the Internet, I have found that some people have graduated with a PhD by means of a “sandwich thesis”. Could anyone explain what it is?
I believe that a sandwich thesis (sometimes called an integrated thesis / stapler thesis) consists of a collection of published or in-press articles (some schools also allow submitted articles). These articles are included in the thesis verbatim. The publications are usually preceded by an elaborate introduction that sets the context for the thesis.
As Willie Wong pointed out, there is also usually a final discussion / conclusion after the integrated papers.
Supplementing GWW's excellent answer somewhat, the "sandwich thesis" or similar concepts, seem to be rising in popularity. For example, in my University, they're afforded equal standing to the more traditional "book"-style thesis, and in my Department, they're the required form of a dissertation.
The reasoning for this is fairly straightforward. In many fields that don't rely on book publishing as the primary means of publication (most of the sciences), the production of a large manuscript-style work is likely a one time event. One can have an extremely successful career without publishing another book, and the mechanisms to publish books on research findings (rather than say methods) may not actually exist.
As such, requiring doctoral students to produce something like that is counter-productive - they gain no experience in the future requirement to publish journal articles, and leave graduate school with a body of work that isn't represented in the journal literature. The idea of the sandwich thesis is to get around this by layering several journal-style publications (either submitted or unsubmitted) as the meat of the sandwich, with an introduction, perhaps a joint high-level methods section and a conclusion section weaving them into a coherent narrative as the bread. This allows the student's work to flow nicely into the literature in a way that's useful to all involved.
What is described here as a sandwich thesis (a collection of published (or intending to be published) articles + Introduction + Discussion) is also called a compilation thesis. In the Netherlands this is a very common format for nearly all science PhD theses. I'm not sure what Peter Green meant by "AIUI lots of people use the "Sandwich thesis" format, while being regular PhD students". Nowadays, most Dutch universities also publish their PhD theses in online public archives.