The justification for annotation was based on the observation that the web is largely controlled by corporations, as measured by the number of pages viewed, who have no mechanism for allowing feedback about the writing. (This was even more true in 2000 than it is now, with the proliferation of web-based forums, many even hosted directly by the big content producers.) Annotation was proposed as a solution to this problem, allowing people to metaphorically gather together on a web page and discuss the content. (The name "Third Voice" presumably comes from the idea that the web visitor is one "voice", the web page author a second voice, and the Third Voice program provided a third voice on the web page.)
Numerous examples of such things were proposed by Third Voice, such as criticizing products, posting reactions to news stories, or carrying on discussions about the contents of the page, but they all boil down to the same thing, discussing the content of the page.