Web 3.0 is a theoretical concept, that still has no actual implementations.
The formal description that most answers here will probably refer to is "semantic web".
But in more simple words, Web 3.0 will provide a user experience in which the "web" will understand what you are looking for when you type in your questions in natural language, and will also rely on the context of your search - for example, what site you are browsing when posting the question, what was the recent sequence of pages you have viewed, what are your past surfing habbits and so on.
Another behavior expected from the would-be Web 3.0 is that the "Web" will automatically and continously discover relations and connections among sites and pages over the Internet based on their content and context, without relying on specific links that humans create between pages. This is a drastic leap of machine intelligence over the web of today - even in the Web 2.0 - all the search engines reply one way or another on links.