How does SSH Agent Forwarding work?

To explain, SSH agent forwarding process here I will take the same example of connecting to Github from a remote server.

When you try to pull code from Github in a remote server with SSH authentication, Github will ask the remote server for authentication verification. In normal cases, the SSH agent responds with key verification using the private key, but in the case of SSH forwarding, it will forward this request to the local computer [SSH client that originally contacted the server] then the SSH Agent of the local computer responds with verification message. When Github gets the message, it verifies the request and lets us pull the code.

Orginal Source: Linux SSH Guide – SSH Key Management, Agent Forwarding