Web 1.0 needs to reload the entire page from the server to update data on the page. Web 2.0 allowed pages to update content without reloading by using AJAX and DOM manipulation.
Web 1.0 was one-to-many publishing, the direct translation to the web of existing pre-web business models. Thus "1.0", the first iteration based on known/previous models.
Web 2.0 was many-to-many publishing, user-generated-content, stuff that wasn't possible or even conceivable prior to the web. Thus "2.0", the second iteration based on characteristics unique/native to the web.
Honestly, people need to stop redefining those terms.