The "Talk" icon creates a new page named "Talk" as a subdirectory of the page from which "Talk" was called. For example, clicking on the "Talk" icon for this page would create a new page named "Talk Pages/Talk."
Talk pages differ from Comments on the main page in that the Talk feature allows users to move discussions about a page off the main page. It provides a forum for discussion of page content that is conceptually separate from the page itself, giving users an area in which to work out conflicts, ask questions, or generally talk with other users who have similar interest in the page subject. Some possible reasons for creating a "Talk" page:
The veracity of some content on a page is disputed. A "Talk" page could be created to discuss the page's content.
A user has a question about something on a page, but does not want to ask the question on the page itself.
A user wants to communicate with other wiki users about the subject of a page, for example: "Is the content on this page true?"
A user is desperately lonely, and wants to "Talk."
All of these and more are valid reasons to create a talk page! It's a part of what builds the wiki community, and what helps keep the information on wikis correct, and up-to-date.
Different wikis have different ideas of what a "Talk" page should be — for instance, some wikis use Talk pages as a place for all opinionated comments — but the above is generally the norm. Wiki administrators can turn off the talk page icon in their wiki settings if they don't want to use such pages on their wiki.