With twitter, it's the ability to post a tweet under a certain username. With owning a tumblr account, it might be something similar. With your known StackExchange profile it might mean posting a statement in a specific part of your profile. And so on.
The common thread in each case is (1) that you post in a place where only your identity can, and (2) what you post is a signed statement claiming a connection among three things: (a) your keybase username, (b) your public key, and (3) the identity on that third party service. (The third one is necessary so it can't be moved elsewhere.) Note how twitter and github's are totally different, but achieving these three things.
We will build out this list of identity checks, hopefully making all kinds of them easy to do. Everything from proving you own a domain to having a tumblr or reddit accoun. The definition of those checks will all be publicly reviewable, both in the spec and in the client, which is what checks them for you.