Sort:  

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?

Public key is like your house address, everybody knows it, and knows it belongs to you. Private key is the actual key to your house, so you should never give it away.

Busy asks for posting keys because they will have to sign the posting transaction on the blockchain, to pair your article with your identity.

AFAIK, the posting key never really goes to Busy over the internet, it stays on your own computer. It is used by the JS library of Busy to sign the transaction locally and then the transaction is broadcasted to the blockchain.

private and public are p2p answer to security, so messages don't get intercepted pretty much how people sent letter with stamps and seals, now think that only the corresponding recipient can remove the seal with his private key, because you sealed with his public key, then you know only he read the message or whoever is the holder of the other key.

It's cryptography and how blockchains work, that's how you get a trustless system, because users are not trusting the system to do anything else than what it is intended, ie. relay messages.

Cheers :)