They want you to sign in using your private posting key, so that they can verify it against your already public posting key. You can think of the public key as the "keyhole/card reader" and the private key as your "physical key/key card".
You can use it to log in on other Steem sites and apps, just remember that the responsibility is with you as a user.
In this case, if someone was to have a look at your private posting key, they would be able to blog and comment using your account. To stop them you would have to change your master key(password), which in turn would change all of the keys including the posting key.
It'd be nice if they were to say "log in with your private posting key"...is that too much to ask?