"EOF from the client" means literally that. Remember that in *nix, everything is a file, including the sockets you use to connect to it (there are two file descriptors per socket connection, ReceiveQueue -- the incoming data from the client -- and SendQueue -- the outgoing data to the client). End of File from client means that the socket has (apparently) been closed from the client's side (RcvQ).
This is not the same error message as "Connection reset by peer", "Ping timeout", "Connection refused", "Software caused connection abort" or any of the other error messages you see occasionally. It means what it says.