Explained simply anamorphic transfers use all of the picture area (576 lines for PAL, 480 lines for NTSC) to display a 16x9 shaped image, rather than the traditional 4x3 shape. This means that with widescreen material you are not encoding the black bars, just the picture - giving more active picture lines.
Widescreen TVs can take advantage of this resolution - by simply presenting the image "as-is" in their 16x9 shaped screen. To display it correctly on a traditional TV the DVD player will cut out extra lines, smooth the remainder, and add in the original black bars at the top and bottom - preserving the original aspect ratio.
Playing with the settings on your DVD player can give a visual representation of it - if you have an anamorphic DVD, and set your DVD player to output a 16x9 image (i.e. not chop out the extra lines), then connect it to a 4x3 TV, the picture will look like it has been stretched vertically.
Hope this explains it - if not drop me an email.
