"Web 2.0" doesn't have any real meaning. It was just a sort of handy label for the sort of look and feel that began to emerge in the mid-2000s when most browsers began to support background requests (XmlHTTPRequest), which was previously only an option in Internet Explorer using an ActiveX component, and at the same time web designers finally began moving away from table-based layouts and font tags to properly using CSS.
Most of what is referred to as "Web 2.0" had more to do with appearance than anything else: large sans-serif fonts, fewer graphics, rounded rectangles everywhere, a lot of gradients, shiny, glassy-looking buttons and more white space on the page than had been used before. That look is pretty dated now, although many of the UX (user experience) principles we worked out in that era are still in use. Pages are still a lot less cluttered than they were before "Web 2.0", but we've moved on to a world where there are a lot more textures on the one hand and a lot of flat (no artificial depth) designs on the other. Trends are trends, and none of them last.
The dynamic HTML part of the "Web 2.0" world is still going strong, though. We stay on a single web page longer now rather than continually reloading/refreshing a page. We are more likely to submit web forms via a background request than by changing the entire page when we submit a form. It's probably this AJAX (background) form submission that you've seen referred to as "Web 2.0 submission". An example is this forum—when you click the "Post Quick Reply" button, the form you use to create a reply in this thread is submitted in the background. You stay on the same page, and when the server has processed the form you submitted, only the part of the page that represents your posting is updated. With a normal HTTP form submission, you would load a whole new page.