What is SSH agent forwarding?

The agent forwarding feature in SSH allows using your local SSH agent to be reached through an existing SSH connection. This way you don’t have to store copies of your private keys on intermediate systems to use them for authentication. While SSH agent forward simplifies things, it also introduces a new risk related to Unix domain socket. If a user on the intermediate system can access the related socket, then it may abuse this connection back to the SSH agent to authenticate on your behalf.

See the ForwardAgent option for more details.