When the web started it was to allow scientist and the like share data. The data was largely stored in tables and this made sense. However once the technology grew beyond the scope of academia, presentation of non data like content became desirable. Because of this tables were hacked to appear invisible and with backgrounds allowing for some extraordinary inventive graphic use. However this was never a tables function and to much information about the content was sacrificed. Meanwhile having t structure and design of the site and the content intertwined is an extremely inefficient way to manage a contiusly growing website.
CSS tableless design allows for a more robust fluid design which means the client can control the content with any danger to the overall look of the site.
It means devices other than your favourite browser can interact with your website, including mobile devices and screen readers.