From what I can tell, you use it to host your blog. People can pay for premium memberships on Medium as a whole and a portion of the money goes to you or something, I'm not too sure.I'm still not exactly sure what kind of site Medium is. Is it a blog host? Is it a social network? Is it a forum? All I really know is that I get google results from it now, and didn't know it existed a couple years ago (if it did at all).
I dunno. I don't like the idea too much. The internet should be decentralized. I guess it's better than posting the same content to one of the locked down social networks, but wordpress is really better.