Basically its a website that is built on an existing platform as a sub-section or sub-domain of the existing website. Thats the easiest way to think of it.
So for example if you go to weebly.com, sign up and create a mini-website on the platform, that is a web 2.0.
When it comes to SEO, web 2.0s serve as an easy way of pushing out backlinks surrounded by contextual content and they are great because they tend to be free, you can add lots of relevant content and style it pretty much like any other website and you have full control over the property once its built.