It is never revealed to anybody. If A and B want to send each other secret messages, then the messages A sends to B should be encrypted with B's public key, and the messages B sends to A should be encrypted with A's public key. If A wants to send B a signed message, A can encrypt the message with A's private key. The methods of public-key encryption are slow, so ssh only uses them for initial connection and to agree on a session key for this conversation. Then the ssh client and server switch to one of several conventional encryption methods such as idea, blowfish, des, 3des, arcfour, or tss for the rest of the conversation, using the session key they have agreed on.
Conventional encryption uses the same key for both encryption and decryption.
The length of a key dictates how easy it is to break the cipher using a brute-force attack, that is, one that just tries all possible keys. A key of only 10 bits requires only 1024 guesses, which can be done in well under a second. A key of 56 bits can be guessed in a few months of time on the Internet. For its first phase, Ssh uses keys of about 1000 bits. It is used for moving files between machines.