For some reason results can be somewhat unpredictable when using sync. Sometimes my books disappear from my reader and sometimes they are duplicated, I've never been too sure why. You can move books manually by clicking and dragging them from the ebook software to the reader.
Collections are folders you can create to organise your books within the ebook software. For example, I have folders for 'classics', 'science fiction', 'children's fiction'. On the reader, books can be sorted by author or title or can be found through collections. I prefer using collections.