Deduplication or extracting unique elements using XSL

When searching for an efficient way to de-duplicate elements in a BPEL process, i found several blogs and communities on the web showing examples how to use the XSL key and generate-id functions to extract unique elements. Only none of them explained the science behind the magic. Here a more elaborate explanation how the extraction of unique elements, based on a chosen combination of key elements, from a XML message works.