Medium is a blogging platform brought to us by Evan Williams and Biz Stone (the two who also brought us Blogger.com and Twitter). The essence of Medium is that it is a minimalist blogging platform very much designed around the written (typed) word. Each member has a personal handle and “/name”, like a Twitter or Facebook page with a photo if you choose. Each post also has a header with an area for an image but the posting format is unmistakably optimized for the written word. Medium is built for idea sharing. The whole premise behind the platform is that the content published on medium is not meant for self promotion or marketing, but for the sole purpose of sharing opinions, ideas, and thoughts.
As of now, you can sign up for Medium with your Twitter account but you can only publish content if you are an invited to do so.
You can browse Medium by categories called “collections” and Medium suggests content that you maybe interested in (I’m assuming the suggested content is based on your Twitter activity). Content publishing is supposed to open up to all members “soon”.
Here is a good introduction video on Medium