The nested tables are not really needed, but it helps to place and align the images/text better then without. It's the ideal solution to put back an image you have sliced into sections, just be sure you can make rows or columns of exact height or width, so there will not be space between the images.
The image used in the left table is to make sure the width of the left table is 60 pixels, this is to ensure that the background doesn't overlap this section. This setup is used widely on the Internet on for example cnn.com and cnet.com. The <td> tag contains it too.