OpenSSH uses OpenSSL for key storage and management, not for transport encryption. That's why it is not vulnerable.
The bug basically allowed someone to craft a Heartbeat message, lie about how large the 'payload' is which would fool OpenSSL into giving up sensitive memory.
It's all due to a poorly thought-out custom memory allocator.
You basically say as an attacker, the payload is 64K, but only provide 1byte of data in your heartbeat packet. OpenSSL creates 64K of memory to store the payload, but only 1byte of it is actually copied into it and overwritten. Because of the bad memory allocator, this would leave around 65355 bytes worth of memory that were never zeroed out. Further, due to the way the memory allocator works, most often this memory being leaked was something that was most recently used and freed up by OpenSSL. This could be any data that is being encrypted/decrypted or it could actually be the keys being used to perform the encryption.